notebooks/python_sklearn_and_r_in_parallel/Forecasting with Python - scikit learn in parallel.ipynb

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    "# Direct Forecasting with `Python` and `R` in `forecastML`\n",
    "### *Nick Redell* nickalusredell@gmail.com\n",
    "### 2020-05-25\n",
    "\n",
    "***\n",
    "\n",
    "# Purpose\n",
    "\n",
    "* The goal of this notebook is to show an end-to-end example workflow for forecasting with both `Python` and `R` in `forecastML`. Along the way, we'll compare the results side-by-side and even ensemble the final `Python` and `R` ML models to produce a single multi-step-ahead forecast.\n",
    "  \n",
    "  \n",
    "* The emphasis will be on training models in parallel. Parallel training may be faster or slower depending on the dataset size and ML models used.\n",
    "  \n",
    "  \n",
    "* This notebook is long because it details a mostly complete workflow for ML forecast model exploration. It's a good template. The aim of `forecastML` has been and will be flexibility so this pipeline doesn't have to be followed in detail. There's a fair amount of customization allowed that could have made this notebook much shorter or much longer.\n",
    "\n",
    "***\n",
    "\n",
    "# Example: `scikit-learn` in `Python` and `R`\n",
    "\n",
    "## Task\n",
    "\n",
    "* **Domain:** Electricity demand in Victoria, Australia\n",
    "* **Number of time series:** 1\n",
    "* **Frequency of data collection:** 30 minutes\n",
    "* **Forecast horizon:** 3-days-ahead\n",
    "* **Method:** Direct forecasting at 3 time horizons--1 day, 2 days, and 3 days ahead\n",
    "* **Model outcome:** Demand\n",
    "* **Model features:** Demand, temperature, holidays, date/time features\n",
    "* **Models:**\n",
    "    + `Python`: LASSO from `sklearn`\n",
    "    + `R`: Random Forest\n",
    "    + Ensemble of `Python` and `R` models\n",
    "\n",
    "## Final Product\n",
    "  \n",
    "<p>\n",
    "  \n",
    "<div>\n",
    "<img src=\"electricity_demand_final_plot.png\"/>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "## `R` Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "options(warn = -1)\n",
    "options(repr.plot.width = 12, repr.plot.height = 6)\n",
    "\n",
    "library(reticulate)  # For working with Python.\n",
    "library(tsibbledata)  # Source of the dataset.\n",
    "library(lubridate)\n",
    "library(ggplot2)\n",
    "library(forecastML)  # v0.9.1\n",
    "library(ranger)  # Random Forest model in R.\n",
    "library(future)  # Parallel model training."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "## Data Preparation in `forecastML`\n",
    "\n",
    "* Load the example data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 5</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Time</th><th scope=col>Demand</th><th scope=col>Temperature</th><th scope=col>Date</th><th scope=col>Holiday</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dttm&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;date&gt;</th><th scope=col>&lt;lgl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>2012-01-01 00:00:00</td><td>4263.366</td><td>21.05</td><td>2012-01-01</td><td>TRUE</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>2012-01-01 00:30:00</td><td>4048.966</td><td>20.70</td><td>2012-01-01</td><td>TRUE</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>2012-01-01 01:00:00</td><td>3877.563</td><td>20.55</td><td>2012-01-01</td><td>TRUE</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>2012-01-01 01:30:00</td><td>4036.230</td><td>20.40</td><td>2012-01-01</td><td>TRUE</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>2012-01-01 02:00:00</td><td>3865.597</td><td>20.25</td><td>2012-01-01</td><td>TRUE</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>2012-01-01 02:30:00</td><td>3694.098</td><td>20.10</td><td>2012-01-01</td><td>TRUE</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 5\n",
       "\\begin{tabular}{r|lllll}\n",
       "  & Time & Demand & Temperature & Date & Holiday\\\\\n",
       "  & <dttm> & <dbl> & <dbl> & <date> & <lgl>\\\\\n",
       "\\hline\n",
       "\t1 & 2012-01-01 00:00:00 & 4263.366 & 21.05 & 2012-01-01 & TRUE\\\\\n",
       "\t2 & 2012-01-01 00:30:00 & 4048.966 & 20.70 & 2012-01-01 & TRUE\\\\\n",
       "\t3 & 2012-01-01 01:00:00 & 3877.563 & 20.55 & 2012-01-01 & TRUE\\\\\n",
       "\t4 & 2012-01-01 01:30:00 & 4036.230 & 20.40 & 2012-01-01 & TRUE\\\\\n",
       "\t5 & 2012-01-01 02:00:00 & 3865.597 & 20.25 & 2012-01-01 & TRUE\\\\\n",
       "\t6 & 2012-01-01 02:30:00 & 3694.098 & 20.10 & 2012-01-01 & TRUE\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 5\n",
       "\n",
       "| <!--/--> | Time &lt;dttm&gt; | Demand &lt;dbl&gt; | Temperature &lt;dbl&gt; | Date &lt;date&gt; | Holiday &lt;lgl&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "| 1 | 2012-01-01 00:00:00 | 4263.366 | 21.05 | 2012-01-01 | TRUE |\n",
       "| 2 | 2012-01-01 00:30:00 | 4048.966 | 20.70 | 2012-01-01 | TRUE |\n",
       "| 3 | 2012-01-01 01:00:00 | 3877.563 | 20.55 | 2012-01-01 | TRUE |\n",
       "| 4 | 2012-01-01 01:30:00 | 4036.230 | 20.40 | 2012-01-01 | TRUE |\n",
       "| 5 | 2012-01-01 02:00:00 | 3865.597 | 20.25 | 2012-01-01 | TRUE |\n",
       "| 6 | 2012-01-01 02:30:00 | 3694.098 | 20.10 | 2012-01-01 | TRUE |\n",
       "\n"
      ],
      "text/plain": [
       "  Time                Demand   Temperature Date       Holiday\n",
       "1 2012-01-01 00:00:00 4263.366 21.05       2012-01-01 TRUE   \n",
       "2 2012-01-01 00:30:00 4048.966 20.70       2012-01-01 TRUE   \n",
       "3 2012-01-01 01:00:00 3877.563 20.55       2012-01-01 TRUE   \n",
       "4 2012-01-01 01:30:00 4036.230 20.40       2012-01-01 TRUE   \n",
       "5 2012-01-01 02:00:00 3865.597 20.25       2012-01-01 TRUE   \n",
       "6 2012-01-01 02:30:00 3694.098 20.10       2012-01-01 TRUE   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data(\"vic_elec\", package = \"tsibbledata\")\n",
    "data <- as.data.frame(vic_elec)\n",
    "\n",
    "head(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Date and time info"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "frequency <- \"30 min\"  # A string that works in base::seq(..., by = 'frequency').\n",
    "\n",
    "records_per_day <- 48  # 48 30-minute periods in a day for easier indexing.\n",
    "\n",
    "data$Time <- as.POSIXct(data$Time, tz = \"UTC\")  # Our date index."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::fill_gaps()`\n",
    "\n",
    "* There are no gaps in data collection in this dataset. If there were, `fill_gaps()` would expand the dataset and auto-fill our date index which is `Time` here. This function also supports multiple time series.\n",
    "\n",
    "<p>\n",
    "\n",
    "* The purpose of `fill_gaps()` is to prepare a dataset to produce temporally correct feature lags. You can use any package or method to fill in `NA` values--or leave them missing if your ML model handles them--so long as the filled-in dataset is a `data.frame`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data <- forecastML::fill_gaps(data, date_col = 1, frequency = frequency)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Date-based feature engineering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 9</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Time</th><th scope=col>Demand</th><th scope=col>Temperature</th><th scope=col>Date</th><th scope=col>Holiday</th><th scope=col>hour</th><th scope=col>weekday</th><th scope=col>month</th><th scope=col>year</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dttm&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;date&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>2012-01-01 00:00:00</td><td>4263.366</td><td>21.05</td><td>2012-01-01</td><td>TRUE</td><td>0</td><td>1</td><td>1</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>2012-01-01 00:30:00</td><td>4048.966</td><td>20.70</td><td>2012-01-01</td><td>TRUE</td><td>0</td><td>1</td><td>1</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>2012-01-01 01:00:00</td><td>3877.563</td><td>20.55</td><td>2012-01-01</td><td>TRUE</td><td>1</td><td>1</td><td>1</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>2012-01-01 01:30:00</td><td>4036.230</td><td>20.40</td><td>2012-01-01</td><td>TRUE</td><td>1</td><td>1</td><td>1</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>2012-01-01 02:00:00</td><td>3865.597</td><td>20.25</td><td>2012-01-01</td><td>TRUE</td><td>2</td><td>1</td><td>1</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>2012-01-01 02:30:00</td><td>3694.098</td><td>20.10</td><td>2012-01-01</td><td>TRUE</td><td>2</td><td>1</td><td>1</td><td>2012</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 9\n",
       "\\begin{tabular}{r|lllllllll}\n",
       "  & Time & Demand & Temperature & Date & Holiday & hour & weekday & month & year\\\\\n",
       "  & <dttm> & <dbl> & <dbl> & <date> & <lgl> & <int> & <fct> & <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & 2012-01-01 00:00:00 & 4263.366 & 21.05 & 2012-01-01 & TRUE & 0 & 1 & 1 & 2012\\\\\n",
       "\t2 & 2012-01-01 00:30:00 & 4048.966 & 20.70 & 2012-01-01 & TRUE & 0 & 1 & 1 & 2012\\\\\n",
       "\t3 & 2012-01-01 01:00:00 & 3877.563 & 20.55 & 2012-01-01 & TRUE & 1 & 1 & 1 & 2012\\\\\n",
       "\t4 & 2012-01-01 01:30:00 & 4036.230 & 20.40 & 2012-01-01 & TRUE & 1 & 1 & 1 & 2012\\\\\n",
       "\t5 & 2012-01-01 02:00:00 & 3865.597 & 20.25 & 2012-01-01 & TRUE & 2 & 1 & 1 & 2012\\\\\n",
       "\t6 & 2012-01-01 02:30:00 & 3694.098 & 20.10 & 2012-01-01 & TRUE & 2 & 1 & 1 & 2012\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 9\n",
       "\n",
       "| <!--/--> | Time &lt;dttm&gt; | Demand &lt;dbl&gt; | Temperature &lt;dbl&gt; | Date &lt;date&gt; | Holiday &lt;lgl&gt; | hour &lt;int&gt; | weekday &lt;fct&gt; | month &lt;fct&gt; | year &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 2012-01-01 00:00:00 | 4263.366 | 21.05 | 2012-01-01 | TRUE | 0 | 1 | 1 | 2012 |\n",
       "| 2 | 2012-01-01 00:30:00 | 4048.966 | 20.70 | 2012-01-01 | TRUE | 0 | 1 | 1 | 2012 |\n",
       "| 3 | 2012-01-01 01:00:00 | 3877.563 | 20.55 | 2012-01-01 | TRUE | 1 | 1 | 1 | 2012 |\n",
       "| 4 | 2012-01-01 01:30:00 | 4036.230 | 20.40 | 2012-01-01 | TRUE | 1 | 1 | 1 | 2012 |\n",
       "| 5 | 2012-01-01 02:00:00 | 3865.597 | 20.25 | 2012-01-01 | TRUE | 2 | 1 | 1 | 2012 |\n",
       "| 6 | 2012-01-01 02:30:00 | 3694.098 | 20.10 | 2012-01-01 | TRUE | 2 | 1 | 1 | 2012 |\n",
       "\n"
      ],
      "text/plain": [
       "  Time                Demand   Temperature Date       Holiday hour weekday\n",
       "1 2012-01-01 00:00:00 4263.366 21.05       2012-01-01 TRUE    0    1      \n",
       "2 2012-01-01 00:30:00 4048.966 20.70       2012-01-01 TRUE    0    1      \n",
       "3 2012-01-01 01:00:00 3877.563 20.55       2012-01-01 TRUE    1    1      \n",
       "4 2012-01-01 01:30:00 4036.230 20.40       2012-01-01 TRUE    1    1      \n",
       "5 2012-01-01 02:00:00 3865.597 20.25       2012-01-01 TRUE    2    1      \n",
       "6 2012-01-01 02:30:00 3694.098 20.10       2012-01-01 TRUE    2    1      \n",
       "  month year\n",
       "1 1     2012\n",
       "2 1     2012\n",
       "3 1     2012\n",
       "4 1     2012\n",
       "5 1     2012\n",
       "6 1     2012"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data$hour <- lubridate::hour(data$Time)\n",
    "data$weekday <- factor(lubridate::wday(data$Time))  # Factor for modeling purposes.\n",
    "data$month <- factor(lubridate::month(data$Time))  # Factor for modeling purposes.\n",
    "data$year <- lubridate::year(data$Time)\n",
    "\n",
    "head(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train/Test split\n",
    "\n",
    "* **Train:** From **2012-01-01 00:00:00** to **2014-12-28 23:30:00**\n",
    "* **Test:**  From **2012-12-29 00:00:00** to **2014-12-31 23:30:00**\n",
    "* **Forecast:**  From **2015-01-01 00:00:00** to **2015-01-03 23:30:00**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_indices <- 1:(nrow(data) - records_per_day * 3)\n",
    "\n",
    "train <- data[train_indices, ]\n",
    "test <- data[-train_indices, ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot time series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YyyAOgv1ZvH7y9f7s6HyFv8Lg6ADglA\ny5UAtOKWIkZZ9suSLjm/dPHJ/p1142f6LZNrB9AhAWi5EoBW3FLEKIt+UOXrw4u7zS96fjx9\nKvrhy9yZXsvk2gF0SNIBLf3YpN+NAVpxSxGjZPUvqgB0SABargSgFbcUMQpARwSg45J+NwZo\nxS1FjALQEQHouKTfjQFacUsRowB0RAA6Lul3Y4BW3FLEKAAdEYCOS/rdGKAVtxQxCkBHpDig\nhR+c9LsxQCtuKWIUgI7IKqBrrUDXAL1t0m8OXS1FjALQEQHouKTfjQFacUsRowB0RAA6Lul3\nY4BW3FLEKAAdkaVAty/kArRTsmkAev8SRhErAeiIAHRc0u/GAK24pYhRADoiQ4x9QHcfgwBo\nN+l3Y4BW3FLEKAAdEYCOS/rdGKAVtxQxCkBHBKDjkn43BmjFLUWMAtARAei4pN+NAVpxSxGj\nAHREADou6XdjgFbcUsQoAB0RgI5L+t0YoBW3FDEKQEcEoOOSfjcGaMUtRYwC0BEB6Lik340B\nWnFLEaPkD7QQCsmBrgG6n/S7MUArbiliFICOCEDHJf1uDNCKW4oYBaAjAtBxSb8bA7TiliJG\nAeiIAHRc0u/GAK24pYhRADoiAB2X9LsxQCtuKWIUgI4IQMcl/W4M0IpbihgFoCMC0HFJvxsD\ntOKWIkYB6IgAdFzS78YArbiliFEAOiIAHZf0uzFAK24pYhSAjghAxyX9bgzQiluKGAWgIwLQ\ncUm/GwO04pYiRgHoiAB0XNLvxgCtuKWIUQA6ImuBjoMOoOVKAFpxSxGjAHREADou6XdjgFbc\nUsQoAB0RgI5L+t0YoBW3FDEKQEcEoOOSfjcGaMUtRYwC0BEB6Lik340BWnFLEaMAdEQAOi7p\nd2OAVtxSxCgAHRGAjkv63RigFbcUMUpuQDsG1O1/4pMAaOdqgB4m/W4M0IpbihgFoCMC0HFJ\nvxsDtOKWIkYB6IhEA71qNoCWKwFoxS1FjKIAaBkVADowAL1wGWJJvzl0tRQxCkBHBKDjkn43\nBmjFLUWMAtARAei4pN+NAVpxSxGjAHREADou6XdjgFbcUsQoAB0RgI5L+t0YoBW3FDFKFkBb\nXgH0bDZ5xtS9UwAdvAyxpN8culqKGAWgIwLQcUm/GwO04pYiRgHoiAB0XNLvxgCtuKWIUQA6\nIgAdl/S7MUArbiliFICOCEDHJf1uDNCKW4oYJUegWwYA2heAlisBaMUtRYwC0BHxAt2CBtBz\nSb8bA7TiliJGAeiIAHRc0u/GAK24pYhRADoiAB2X9LsxQCtuKWIUgI4IQMcl/W4M0IpbihgF\noCMC0HFJvxsDtOKWIkYB6IgcH+gaoGeXIZb0m0NXSxGjAHREADou6XdjgFbcUsQoAB0RgI5L\n+t0YoBW3FDEKQEcEoOOSfjcGaMUtRYwC0BEB6Lik340BWnFLEaMAdEQAOi7pd2OAVtxSxCgA\nHZFwoGuA9iT9bgzQiluKGAWgIwLQcUm/GwO04pYiRgHo9akBOi7pd2OAVtxSxCgAvT4AHZn0\nuzFAK24pYhSAXh+Ajkz63RigFbcUMQpArw9ARyb9bgzQiluKGAWg1wegI5N+NwZoxS1FjALQ\n67ME6Fo70DVAb530m0NXSxGjAPT6AHRk0u/GAK24pYhRAHp9jg90DdDzyxBL+s2hq6WIUQB6\nfQA6Mul3Y4BW3FLEKAC9PgAdmfS7MUArbililJ2AfprMbff19rY7ezlxe+u9TwZp1uzWuey2\nvcy6+va2HezlxK01cCa59Zy6rPZ1npe1zvihWJsfA5+hhKQJR9DrwxF0ZNIfZ3EErbiliFEA\nen0AOjLpd2OAVtxSxCgAvT5jQDc4A/RM0u/GAK24pYhR8ga6NgA9CEDLlQC04pYiRgHo9QHo\nyKTfjQFacUsRowD0+gB0ZNLvxgCtuKWIUUoA+rwAgJ4MQK9ehljSbw5dLUWMAtARy10JdA3Q\nxirZOAC9fwmjiJUAdMRyywY6Xuv0uzFAK24pYhSAjlguQMcl/W4M0IpbihgFoCOWC9BxsScR\nfvXEXzIIQCtuKWIUVUCv3InPZOYCdB0F9OkOAL26ZBCAVtxSxCgAvT4AHRmA3r+FUXJsAWiA\nnl+wfWoF0MsfHYDev4VRcmwBaICeX7B9CqCDlyEWVMuwJPUoAL0+S4GuVQNdA/TGQbUMS1KP\nAtDrA9AjiwgNQO/fwig5tpQIdHc/gA5bsH0KoIOXIRZUy7Ak9SiFAx3FAkCPLCI0AL1/C6Pk\n2FI00DVAhy3YPgXQwcsQC6plWJJ6FIBeH4AeWURoAHr/FkbJsUUV0DVAj1cagI4oGQSgFbcU\nMUrBQFuGrsvOQDeLPCDQNUDv1cIoObYANEDPL9w+1QO63hroGqBTU6CupYhRCgG6Buj5hdun\nADp4GWJBtQxLUo8C0OsD0COLCM0I0LJWA/T+JYwiVnJIoOv2zuevRwRa+oAzKdDtouuVCwop\n8QagFbcUMQpAr08GQItZBtCrlyEWVMuwJPUoAL0+ewN9XbQDtBRmAL16GWJBtQxLUo9SLNC1\naqBrgF5a4g1AK24pYpSygY7zDaBHFhGaJ9NsHYDeq4VRcmwBaICeWXjv1BjQte8u/vPzAej9\nWxglxxaA7kra2+wNdA3QvVyBrgF6vxZGybFlCdA3/Qj0AzRAe+IA3W0xgNZewihiJeUCXQO0\nvfDeKYAOXoZYUC3DktSjHBzo2gP0VYH9gK4lgK6ngY6lDaBXL0MsqJZhSepRxl6Dfl19/GbM\nt/9VryX6lwBdbwV0z7JDAr16HoBevQyxoFqGJalHGQH63zd/XU78dfNOoB+gpYCuAXpFyWgA\nWnFLEaOMAF21524qgf6MgY7QAKBHFhEaD9DWdhMKQO9fwihiJSNA33RH0Hu/Bi0H9FVgH9B1\nqwJA99ZkD6Br071YA9C7tjBKji2LgX51U318+fLtY3XzSqAfoAG6d1OATtPCKDm2LAb6f92H\nOP4n0B8HdHc+sK6733GB7omsEegaoPdvYZQcW5Z/iuNd47PEe4QADdD9mwJ0mhZGybFlxY96\nf/6lurl59e4vkX6AXgV07ZwG6FUB6P1LGEWsJL/fxRELdN3aPAS6bpZiAb2eA4AeXdv5NoBO\n08IoObYA9BXozk6AHqnaE2j7EQJoVMuwJPUoY0B/fp3qR70B2h7FOg3QqwLQ+5cwiljJCNCf\n0/wujhqge6NYpwF6VQB6/xJGESsZAfo1QAc0OUDXl1G2ANpe43Gga6MN6FuA3r2FUXJsWfGT\nhL98E+zfHmgHmBboGqBDZ+mdAujgZYgF1TIsST3KKNCi/XkAXZtWARVA19YCrDWWB7rOD2g5\npAF6/xJGESuZ/WVJItkX6HoW6Pp4QNcA7Q9A71/CKGIlI0D/dvNRsh+g9wJ61TQADdAKW4oY\nZeIX9gv2A/RioK3j4dp1DKAXBaD3L2EUsZLR16CVfYqjs3Ix0A6zS7Ic6PZU0EBDoOs0QNc7\nAd1su3rNozEWgN6/hFHESg4IdN1oAtChgwA0QOtrKWIUgNYCdLsIH9A1QI8FoPcvYRSxkrx+\nF0cioOuZhY91TgJdRwJdW/rOAN1OoQToGqCTtTBKji0AfWSgu80G0MMA9P4ljCJWAtAAnRfQ\ndSTQ/XsC9P4ljCJWMgv0X78I9AP0OqCtI0ov0LU80PVeQNd+oGuA1l/CKGIlY0B/TPLrRrcD\n+gUDnUDXHqDbtzb3BbrdVOY64mApoX0d0PbDANBHKWEUsZKj/LpRgD4M0DVAay9hFLGSEaD/\n0fL86m+BfoDeFmhr4YunMHsD3Q4F0AlaGCXHlhWfg/7NvL752/z9WuSXcmQEdJ0R0FOcAvTK\nAHT6EkYRK5n4daP/vvmfMX/dvBbo3w/o1pKlQK+gLROga2fhi6cwKYF2HimAPkoJo4iVTAD9\n+eYXI/SboeeA7vHaXLEM6NpawgTQvj9mGsuxzg2B7lYva6BrdymeBfsuDAF6tdAAnb6EUcRK\nRoB+dfPNfLu5+cv8BtDjnQC9Auh6FOgaoA9SwihiJaO/D/r139d/mHCPlzg2ALq/69/63QZo\ncwiga88pY00yEoBW3FLEKKO/D/rlyPnyWbvPAv35Ae1ebZaL0N6lLgvobthdgA6dB6BzKmEU\nsZLRnyT87ZUxH1/dvJLweVugr0weBOj2KoAeW8LICCOdAL1/CaOIleTxuziODLSDKEAPge4/\nUgCtvoRRxEoAGqA3BNp/2SzQbQ9AqyxhFLESTUCP6CMAdD268KnMAN1YJg30bW0DbQ18QKCD\n5xkC3XwF6P1LGEWsZAzoz7v+sqTkQNfhFFjFaYGu5YCuAXpy6UVQoK6liFHy+GVJcUBfpQgG\n2nc1QDtDTQFt47wcaGsogE7Qwig5tiwG+nVioK3dMxDoGqAB2j4F0OlKGEWsZOKXJQkmH6Dr\nkasFga4Burcw+2w3VB0EdOBAAJ1TCaOIlUz8Lg5PHt9W1ZtPl9NfHqrq7uHr3Jleiy+3U0B3\nnAH0DNB1uGeDQXIHem4ugM6phFHESkaA/uXmL8+N76tz3p5OP15OV4/TZ/otviwBekwBgN4F\n6HpHoJ1vn+YGA+icShhFrGQE6L8rz48QfqjevhwWf3lTfXg5c1c9fDffH6o7M3mm3+JLJkAv\ntg2gZ4Durw5Ap29hlBxbln/M7h/DNwm/V9X309evJ3ofq4fzhffVl6kzgxZfANpeqGnvZVkG\n0ACtqIRRxEpGf5vdEOg/q/fdDd5fX8F4PF04fmbQ4osA0C0chwC6Q1kR0J7qIdDOUACdoIVR\ncmxZDPQrD9D3lfW+X3Pma3U/dWbQ4gtA2wu1DzSnga4Bulv0YD0AOl0Jo4iVLPiY3ZvKfH2o\nqrfnVy6q6nrp6cT4mUGLLwBtLxSgAVp7CaOIlYweQQ9vWlXXz2e8NwuA/vGcp6nc3t42J06n\nT+dum/NPt+21T90VvbtfFnFrLeGSJ+uPJ0/9Pwtzucdts7LNLOeLuwXeNlPcWqfsBfQWag10\n/vPUm8C+6tZz1Yrc3nbb1VlC+2g4W+06bPPHd8cnZxNYixt5SPoXN6s0uancsv56BG2JDuiQ\nWxOyd0Zfg/7mAbr68N2Yx7vTu3/HPYIOPwbd5gjaOWrWfAQ9XJ3+ofLwCNo6zxG03hJGESsZ\n/RdVXg8+ZldVlx9ROX9MI1ugxwQOA7pu/h8SgAZoyaBahiWpRxl9DXr4JmGgyWUCXbtA14cA\nul1ngN4jqJZhSepRFgD91pb3vno+n36+fHBj7MygxZdooGuAVgD0YHsDdIIWRsmxRQTo91d5\nzekHVd5ffwzly+Wjz2NnBi2+HB/orhKgATppC6Pk2LL8NWhPvlx/RPD8EyiP1+Pj+9OPpYyf\nGbT4AtDuQo8CdO2uDkDPBNUyLEk9ypJ/8urt+Zj48e58JJ3T7+JIC3QN0N5hAHphUC3DktSj\njAL97d+vb26M81mO5zfWr6n7VAWd6bf4AtDuQuWADh8EoKdSBAXqWooYZQzoj9X55eebm3f2\npZ9eiG5+0fPj6ZePPnyZO9Nr8UUN0L3LAXoJ0MPtvQnQ3T2uFwD0/iWMIlYy9utGr+8Pvvz5\nKNCfP9B1ANB9JAA6AGh7weFAW4/n+KbyTgrQGZQwiljJCNDvbqrPp39W5dvrm38I9AN0AqAn\nvhXwdPaG1AB07TsN0BmUMIpYyQjQ1elfVDl9wu7bDv9o7BDo1raFQE8IDNDj6bY4QHtTBAXq\nWooYZerfJOz+ExuAbivaKs8C220A0NboY5uqW2V7Rbp7XC8E6P1LGEWsZO4I+vNNNbjP8uwE\n9JTAa4GeIEga6Lq9dSDQ7RTOQNbiABqgU5QwiljJ6D8aW308Af2xuvlFoH8PoD1RBXQ9AnQf\nL4DuFwJ0biWMIlYy/SmOU3z/vPfSrAfa4gygL3dVBrS14P5AoUDXI99s2Ges1nZ1ADpRCaOI\nlYx+DrrxWeJTdoqAvry0ay/dLuoXm/YIH6D9QFuzAvRMUC3DktSjjP8k4btXNzev3g1/b/+a\n6APaZs5Y/W6xkQW6hdkMVs1a6yVAhwkN0ACtsKWIUZb8Lo71Aei2wkXLXlo80Jez1poDNECn\nKGEUsZKcgW53WtNe7Xv1Ybhv93d7gJ5OlkC3FwO0uhJGESvxA/3xl1c3NzevfhF5AdokB9rF\nYHD1FNC1JcMhge6mdtYpHmhrZmszjADtGaR9hABaXQmjiJX4gP5ctR/hqGSIXgO0pZCxrrbu\ntxXQ9l8EtdWYAGgPXvkBXdt3tLZOt1m7zQDQiVsYJceWRUB/vLGT7FMcqoCuY4GuNwC6Hqyx\ntdXss1qBrq0zVm27OgCdqIRRxEqGQJ8+Av3q4+nTG/DMuAgAACAASURBVN8+vn45LfE5DoBu\nK1y0rFl2A9p7LLox0AOcATpRC6Pk2LIE6HcvPrcX/qP3C6FXRh5oa6f079v93T47oF110gBd\nRwHdbCaAlgmqZViSepQh0K/tlzU+39y8FujfAOhOB/++3c8E0JYk64CuARqg44NqGZakHmUI\ntPuqxk2y32YH0H68NAI9xBmgE7UwSo4tC4G2ri8K6Foc6D61U0A3V/uA9kySM9DthmlmHeI8\nfEyiga7tBwygE5YwilgJQPeESAV0d7UQ0HWtH2jvprIKrDPNTZpLATphCaOIlQB0T4gsgJ4c\nqgf0YChrzY8AdPtUcIawHxqAzq2EUcRKtAM9bZmVcoBuN6YQ0DVAF0GBupYiRvEC7UagXxro\nut3/AHo4VLfmTdFgrZvT+wDdG0oU6GYEgM6ohFHESgC6J8SxgXZL8wJ6LACtroRRxEp0Ad3u\nfWJAD84fGejaLrV10wt0+zwA6IxKGEWsJN9fN5oR0N3qOVEEdLvZANoJQCtuKWIUgO6dVwP0\nSAAaoJOXMIpYSclADyTo/jMLdCNUjkDXptt6xgD0RABacUsRo2QGtIWMvS9bV19ONftff5cf\nD0BvA3S7eequx3SD+oYC6IQtjJJjizKgOxUAeukkPaA7v0wHtN0P0O4Jb4qgQF1LEaNkDHT3\n3zKBXjcJQAN08hJGESsB6F4lQJ+/rAXa0tGZOQbo2gLa+lIDdK4ljCJWAtD9yrrd8a+dAD0K\ndL0K6MBJrIkAWlcJo4iVALTXhD7Q132/W2eA3g3obqh2EGs4gM6whFHESlQCXe8DdHeYBtB2\ngTEAvUVQLcOS1KOoA9oCZWS390ce6GZd6pVA1/YCrauPBrT/9ef5SYZDtYMAdN4ljCJWohDo\neh+g6y2BtqB0ZgPoqaG6h6AbDqAzLGEUsZKcgB7sk+NANzunb7f3ZxHQ9c5AO1cD9NhQxlpz\ngM64hFHESrIFutsz69q5Pg3Qlj6XdZEE2r0aoKeHAujsSxhFrASgx0UA6GaRoUDXAB0RVMuw\nJPUoGoFuLtoQ6EuRiQe6t3qJgG424NGB7q9CO8nsExOg9bUUMYoeoJvTAD2z1r1NUybQzQ0B\nOkUJo4iVAPSECuaAQNcA7XtiArS+liJGyRxoSwWADppkGdDNDIJA191pe5V8gwH0/i2MkmPL\nAYBu922FQFvL3Ado+w9AhzwxAVpfSxGjAPREZytCLQ90rRdo54URgBYLqmVYknoUgJ7oBOh2\nQzgF00DX7emRVQqcpD8UQKspYRSxEoCe6DwU0LUNdMucQqDtzQTQWZYwiliJPqDbi4z34rGU\nDrQ9UHdxO5i1Kucv0UB7Vqmue4MB9P4tjJJjC0AXDXR7dhro6zjnNVoE9JXEMaCb1bK/BkzS\nH2oK6Ka0B/TpJEDvX8IoYiUAPdG5E9C9q5UA3Y3dlCQAupsEoDMqYRSxEoCe6HSA7g54z+uq\nBmj7pAt009nexKwG2nEToNcF1TIsST0KQE90FgF0PQu0uzrJgK5Hge5Kre92ADpdCaOIlQD0\nbCdABwJt+zkG9IJJBkMBtJYSRhErAejZzgbo2gd0e9NcgHbWvFk1zx+FQDsFAJ1xCaOIlQD0\nbOfGQNu3MNZVEZPYS9gY6BqgxYJqGZakHgWgZztNe+66mpd13Qxo58SqSQAaoJOWMIpYCUDP\ndu4ItNO9fpJDA12HAN2uGECnKGEUsRKAnu20gL7gdVnXUoGuMwDauQygsythFLESgJ7s7L5a\nQFswSwA91e0LQAN05iWMIlYC0JOd3dfmv0FA144dvZW2bzI2dWZA95ffB9pdOECvC6plWJJ6\nFMVA+y8eC0D3gbbX6WBAd3MBdIoSRhErAejJTvvr5TRA2/foivYE2r0MoLMrYRSxkmyArgHa\n0+1L9kDXg7Fjge4P5RQCdHYljCJWkg/QkyjlBnRztmygfZ27Ad1eBtDZlTCKWAlAT3baX6/n\nlgDtv7d1kzEEAXpY6lkKQOdZwihiJRkBvXDvTAS0qx9A9zuTAN2tkwV0DdCpShhFrASgJzvt\nr55V0QG0b5WOAXSzMt06AXQOJYwiVgLQswHowfJzBLr2zWwAOkUJo4iVAPRslgM9vnoAvWwS\nT4FvZeqxmQ1ApyhhFLESgJ5NHNC9O+cNdB0G9JjAAB0VVMuwJPUoAD2bKaC7r2FAO/dUDfRY\nJ0CvDqplWJJ6lEyAnmMWoLsAtHv5EOjuHgagU5QwilgJQM8GoENWD6Cjg2oZlqQeBaBnUw7Q\nzVUA3UsRFKhrKWIUgJ5NANA1QM8A7c3ixwSgdZQwiljJTkA/TeX2Jef/jOdpeJMn/8XyGent\nXfV0+t/Tk/dmnoVdr34aWfu4oZ6Gp5/6f6w1fepf9XQeZWzd/KvXK9jmUfEt9bqa/mfI5PPu\nJT+GPUMJSRSOoGcTfARd53QE7TnNEfT4E5MjaH0tRYwC0LMB6JDVA+jooFqGJalHAejZ6Aa6\nd7EP6MFVAN1LERSoayliFICeDUCHFOQKdA3Q+5cwilgJQM9GFOje1QC9KF6g3X73GoBOUsIo\nYiUAPZujAz28CqB7KYICdS1FjALQSwPQIUAHBaD3b2GUHFsAenOga4AG6LigWoYlqUcB6KUB\naIDeJqiWYUnqUQB6aQAaoLcJqmVYknqUXIAO2DMB+hKA9l0G0BmVMIpYCUAvTSDQg6u9S5n7\nhwp8AWjfZQCdUQmjiJUA9NIANEBvE1TLsCT1KPqBDgxAA/TEExOg9bUUMQpAr8nhgHauNgDd\nSxEUqGspYhSAXhOAnl747BpeAtD7tzBKji0ADdCzhgL0aIqgQF1LEaMA9JoA9NKFewPQ+7cw\nSo4tAJ0p0EsmaALQvssAOqMSRhErAeg1AeilC/cGoPdvYZQcWwB6J6BvvTcbWQJAB95uqtcG\nengNQCcpYRSxEoCOSalAzyw8NAC9fwuj5NgC0AAdDPRJ6OVAO0sIDEDv38IoObYANEAD9NQT\nE6D1tRQxim6gF2QToJ0A9NI7iAA9fhVApyphFLESJUB7dkGAnlz48l6AHk0RFKhrKWIUvUAv\nDEDP9cYDvTQAvX8Lo+TYAtAAPdsL0KMpggJ1LUWMAtBiAeilAej9WxglxxaABujZXoAeTREU\nqGspYhSAFosaoEduAtCjKYICdS1FjALQYskH6ImUBHQN0IlKGEWsBKDFshjomZuMRWQSnUBP\nBKAzKmEUsRKAFsvhgJbomQxA79/CKDm2ADRA+/t7FwG0N0VQoK6liFEAWiwAvTQAvX8Lo+TY\nAtAA7e/3XXyiGaDtFEGBupYiRgFosbwAXR8H6OYWWzIN0Pu3MEqOLQAN0P5+38UA3U8RFKhr\nKWIUgBbLIqAX3KQfgPYFoDMqYRSxEoAWC0AvDUDv38IoObYANEAH9ZrmvwBtpwgK1LUUMQpA\niwWglwag929hlBxbABqgg3oB2ps9dtLr5ti6pgjV1LUANEAHBaC92Xonvazq+bPnGzeVoZq6\nFoAG6KAAtDcb7qTX1Wxbtha6CNXUtQA0QAcFoL3ZZCdt1tBtAei8SlKPAtBiAeilKRloz6vN\nl5aNhS5CNXUtAA3QQQFob+R3Uh/DAJ1hSepRAFosAL005QLtVRigMyxJPQpAiwWgl6ZYoP0I\nP01dKZUiVFPXAtAAHZQW6Fv3km0C0L4WgM6pJLwl5jPsAA3QQdELtD95Aj2yJz9NXy2TzFTL\nviS05bz/b1AC0GJZBfSKAHR4sgR6bEcOB3oTCiRTHNB1+x/hEoAWC0AvDUB7W2b385iDtZxU\n01AS1lJb/5UtAWixDIHeJntMAtBORCkY3Y2fZm/RXg3Qe5UsAXr9wwLQAL0gAN1LVkDHfTed\nkWrnHOLVmrr3VbBEEdBx2YU1gF6UIoEe34mfAm4TfbCWj2rnHOLVmtpzSqoEoMVyHKBrgHYj\nSMHELhwEdOzBWjaqnVObI3wzANACAeh1JQBtJCmY2oOtlvGb1fM3mUw2qp0S995aLqPUI6dF\nSgBaLAC9umSz5Ab05P4bAnQdcJvJ5KLaKZHfDWQySj1xLr4EoMUC0KtLNktmQE/vvXbLyC3r\n0TOhyUS1U2JfGchklHrybGwJQIsFoFeXbJa8gJ7Zd5cCvcqCTFQ7xf5uQO8ogzWXHQWgxQLQ\nq0s2i1qg/bftX7jCgjxUOyX6L5s8RhmuuOgoAC0WgF5dslmyAnpux50FWsKCPFQ7JfqlgSxG\nCXuc1pcAtFgAenXJZtELtOdbZ8/9lap2SvxLA1mMAtBCAeh1JQBthCiY3W17LUFHmDpVO+UY\nQG/+qAC0WAB6dclmOQzQY++iqVTtFIFvB3IYBaClAtDrSgDayFAwv9P2W6yPoQX84EpgclDt\nFIGXBjIYZWyN5R4VgBYLQK8u2SxCQN8uebKPZDnQQT/IoRTooA+pxJaIZKol5OeJIksAWiwA\nvbpks+gGOuhHodWpdorICzbpRwFouQD0uhKANiJAB+yynjUN+GVCqYH29q/46MP0FStKhDLR\nEvA7raJLAFosAL26ZLNIvQa9+jeutVkHdMiv40x72OlfQYCWKgFosQD06pLNoh7ogPslBbr2\n96/56MPcVQtLpDLeMrmu4YPUkyUALRaAXl2yWfQDLbPo+JKJak//qo8+eK6cvClAi6UIoPdq\nAejwZAN0yAL0AV2PrcCqd9aG106/wCPx1u18RkeReu8WoM8B6HUlAG1O+0+s0FsCnep1gfbT\n2Y3T3VZf98Jt//raLhneMC3QC+aYvyFAA/TKEuVA1yUAvWTt5P7tAVvSy8buzk7YueBNz8lP\nGdZpj6DF3rutJ0rMCqC/VNX1xENV3T18nTvTa/EFoLPrAGgn0UAH3V0K6F1euJ2e6Gn0wDdg\nS/QPzMduJPDOgLPE2rvS/g22YIyQmwkCfXcF+rG65HH6TL/FF4DOrgOgneQOtLP86RdudwJ6\n7LWJoA1xeWmjts/6biIH9OW50pyonVVf+dmaVEB/qK5A31UP3833h+pu+ky/xReAzq7jKEDX\nUkBHCr010L1XbifqhF4XmBnoyX+b0H84pa7dv3H8/VJAe9bKWgHfjw+FFS+4lRjQX6vrEfRj\n9XC+4L76MnVm0OILQGfXAdBO8gfaOMeb43VS76yFAH2BrHkc5u+0pEsQ6LHXuK+Xj/0A/uoF\n+24lBvSb6voa9PvrKxiP1fupM4MWXwA6uw6AdhILdNidRYCefGNN7J21uYGaUWrrhYpV/+7g\nWNvlow8SQk/8Zea1c8EYwa/niAH9qbo3F6Dvq8ubgF9fLpk4M2jxBaCz6wBoJwqA7r2lNvrR\nB5nDzlCgZeJ5CeJSsi3Qvk/ALfpbZnegn6u771egm89ynE+Mnxm0+LLDfmoAemUJQJvL/hOB\nQeBdI1W7jDtZKfXRh9llyP9AuecCEaCnF/GyPZ/sc8sKw99KFAL6vvrTLAX6x3OepnK7ffbo\nOGbUb7nJp14H9OTNzs/S2VvI3zMivtLbsSskFr5lBn23Uusxu4TrM2j+qbRq6fM3WQL0n9Vb\nsxjo3l8DvnAEnV3H/kfQm/WkP4IOvecWP4U9uEziCHp+ETsdQe/x80NPYx+Qllm84BH097vq\n2SgGektqmhwbaOktWAbQwXfcB2iB1wV2B3rQuCvQmy5fEOiH6tPpC0BPBKBXlWyw7DZi/ybh\ndkdRdotYtvvow9aqBVQKAR1ydz1AV11OL0c/ny98vnxwY+zMoMUXgA6PAeiFAWjnEoAeX6o3\nIp+tmbuBPNDvrz+G8uXy0eexM4MWXwA6PAC9NImBXnAvJUBvftg5X9qptnaY8B+c0QP0Nc1P\nEl6Oj+9PP5YyfmbQ4ssW4pj+WYBelJRAy9aUCvRm76wdA+jgz8zFfvhxcMJ3tTzQm/wuDsE9\n0we0mbqFTAB6VUkN0EYL0Dscds62RgO946PS/BYmf+d2QH+yf2fd+Jl+iy8bAG0AOi6HAXp6\nB1sC9DoMAFom9fCMDqA7nMc+WDNZshpo83j/gvDDl7kzvRZfADo8AL0wiYFech8V76zt8rrA\nXK/1wq2K72vq0dYNgF4TgBaJ6YDe+gX1/YG2/sUkyQ6Ads/GvbNW7/PCra97eGY90KkelZE3\nbgEaoJcGoO0AtG+BE9kWaFs1VUCPvOwE0F6gtzAOoFeV1C7Qkj2CQK/AYNE9eGctsB2gpZMU\n6PMHagB6WfqPidmiFKB9LXIpAeg1wyR8VLzf1QB0H2hTA/R0ANrOwYDW8c7aeDtAS2cB0DI7\nZ85Ar+8tAGjxRyYp0MvukPk7a4mBtuoVA+39S7NQoJslzQAtqs7uQG8FNUDbaZaxFINDAZ3y\n/U63PxLopI9K4UC3bk0AbQZAy4FwOKANQJtjAK33nbXBCrjvrCn7vsbzmGgHesH+2ge6+wPQ\ni5IcaKmuooE+xkcf+mvQO+xUBvTwO4HJkqyBXv4iRCjQBqCnA9B2VgK98Oa8sxa2DpFAp35U\n+t8ITJeUAPRpS5yBbg24bJz2LpqANkcC2lr4pcjkDfTCnTs1BYcD+rISyoHufyMwXXJkoM0Q\n6GvDYYEWmyQboGM7ywb6IB99sNbi8ixxSlR+X1M7q6EV6G6nDdxZA4C+bh8D0FMBaDvrgF6q\nYNZAJ385fbxk0781twG67q1FOUCb7msA0NatZJIM6OXfbExnP6C7R6n57+XhaVYgsqNwoNuV\nUP7O2lSJOqCH61Aq0AagV2YXoJ9mgJZ4LVoW6EW7dw4UtN9LA/SqW+88yjAZAt3tkiuB7gSe\nAdpsB/TEIgG6yQBo4wBtAFokdfsfc0igFX5fE16SI9AdyN1O214/szv2gW5FXgv0MiAAekla\noI1F82GAXmzgnu+sLV25hbfPF+h8HpWwkgMCbfxAG3NAoPsv1aoE2gB0r2XDqP3ow0QJQMcm\nFGizAdAmBOhxpRMDbc9uAHp5hIFesIPnTcGRgD7OX5vDAPT50p2AXs5cCNCWY/qBNgC9aQ75\nzhpAR2Y90OcbtOfnd8dpoAdXJwF6ySJ7QJvSgF60sXxJBvRiCQB6dcmGf2sCtAdo050/36C9\nfn53XA20GaEgJdBmBOjuLzG9QJ+WtQTotd3SQAfv4rlTsGj9Mgf6MH9tDnMkoM2xgW7W+uBA\n994eAGjZAPT6lu0C0H2gjXP1cYCWMjQ90Nbr0DHdAD1SsmT9Fs8C0FIleQLtUBsOtLHutRbo\nfoc40NY8o7fpTi4BWuIl2yZ+oBcvffwORwd6uQT5vnCbP9DHeVT6OSzQ5/tZf5YAbffsDbR9\n7QjQRjvQzQr3gG4e7e5PjkAH7uT5UwDQi1s2i3KgA3fSEKBNOqDNEYBeuPx5oM0qoMNXA6DH\nSgB6cctmAegpoE0yoH238gHdbBeAnlyutwugx0qCV3H5LPurFrSOKx4UgHaA7kReC7T/ELkD\n2gyvngU6nINNgDbHBtpYD0PvUfMDbZY8IvJAB+3mGigA6MUtW+U4QE/tmeuBNnkD3X5noRpo\na2yzGGjvNxZBawDQYyXFAb3mQQHowwNt+9kMObyVNYR9zyCgTQu1IqDNRkD3rkoDtAoKDgX0\nYR6VXjIFuvdqcsCeaXPrE3gl0KZ3foKCU8KA9n3f7hRa9zAN0O1aukA3m6ljLzwTNwZoO71l\nzO/oOigIXMsVwwC0VEk+QJsB0N1Z/57p7IoCQJtmoTJA22stBPT5roJAj996O6CtNe0D7T4s\nS4A23pPnswA9WnIooOdXc9WDAtB+oE0faIu4dt+zjsnWAu1cVnc9TodPJf9hnO3aFNBmUNQf\nahRoIwC0R72JQdqv2wFt+g+FCQTaOF88QyUBWgkFAL28ZZscH2hX4+ESbKDtq53TddfjdAgA\nbeKAttc1F6BDqsSBdv6mcxba1mwP9OyuroWCoPVcM0yOQK97UAB6BdBDX9ybe5bg2wRrgW50\n2AzoBsMWKWddnxYAPYLoGqBNVkA3V2UJtBoKDgX0YR4VJ5qAHuyVA6B7kQbaRmIx0J28lyoJ\noK0h23u4SxsW2IPMAe2sdfs3wfSy+8MMSrcEevh3FEBPlISs6KphAFqqJA+g291uFOj+n97u\nb0a3/wTQg5udRXLpMT1qWySGF5/iBbo11EwBbdx7AnT3eFtLygPomZ1dDwUBa6oH6OlVXfmg\nAHQ80N7d3F7KKSHbubYcbYnxAG3B0VNoM6CtPDUSmy2ANvYgo0CPHP4PFiYJtLGKswZaEQXz\nq7puGICWKskEaLMW6I72kYgB7YrcA7q5hw6g+3/D9YjrBokC2t1K9oDNGj959xoNQE/u7ooo\nAOjlLVtELdDNyZ2BthSygHZ6NwTazALdLKEZ0AbaAbHHbs8wWaA952eBnnrEQoBuJxkO11yy\nO9BrJeCjD9ElR3lUrGQBtOmAtiIDdJNYoM0AaGO57QG6hWIF0O1EeQBtEgNtVgF9ucdGQE/s\n8KooAOjlLRsEoGOAboBaB7Rxge4m6pkWCXS75pNAN9u5G8Sp7yaRBdpY11trKwS0cefrLgbo\n2ZJjAT2+uqsfFIDODujLKWmgrQUZY635xkA7R5jGA7RD+OZAm3bA8cfEBtraBt0ajgPdu3hL\noEd3eV0UzKzt2mEAWqpEB9AuFNkB3al428EoBfTguRUMtE1xuyrrgTbWVNFATzwmAL1lln14\nWBvQR3lUuhwC6JDNH7ide0Bb3U5vd3Yt0A0tvVcfFgBt3Jv4gDYW0MPD4KVAW9ugv/LN0iSA\nth6KCaC7VauNvezdgB550q2XAKAFSkZWWNuj0iUXoM30cfAAaJMK6JaYq34eoPsKbg+0sW+9\nG9DWvQOAtrdW0GPSA9oYe6EALVQyub6rh0mn2jEelS7ZAG0p4Im1R+YFdE/F256C7T3tBVmn\nLRQ3A9pda2GgLZSngLbQXAX05YJFQDcP4mZAe591ERJk+OHhowCt71FpA9AjfQuB7lzrLu4D\nbc/o8tJZZi3Ynt0ziRTQxtJ1HdDW0maA7v2NMwu0ezIUaOdFkQ2BHj7tpp7C88kO6PXTJFTN\ns9IKH5U2GQE991TZF+jWywHQ3erEAe2ILwh0e0wcAHQnrgzQttGjQAc+JvqAjoIgww8PqwTa\n89fmFi2yAehVQHffYq8C2iH3utwsgW4PpMOBttY6C6CN76qtge49NJE+A7RMCUAvj3agHU/t\ni5YC7bAqDnS75h6g3TW2D+6ti1YB3UOyA7r3SC0F2h3KLAPa7A90rM/ZfXg4YqCkqg33iC1a\nRAPQK4C218i1bAJo9+IEQJtmobVb4i7YA7TNbRTQZhTo/touBdp7mNwM1wPa7AG075FdH4CW\nKaknzsm1iCZvoJu1WwG0MZsC7evPDWjPyjtL8gJtl20EdLtwMaAHCnuAtkt2BTre59w+PBwz\nUVrV6pHTsi2SAeiNgLavWge09cc6/tsD6PG/deKB9j1SMkD3ngbucG7JDkBft0xd16O3CE9e\nQEdNBNBSJQA91jcA2mwEtIXkNkCbnmHG9NZ8DGjn7xBr6UOg2z95AW02B/qyPebWPyxZfXg4\nbqbEqtWeU/ItgtEB9ERsz0zWQDs32xLoiZU/HNBd93DNUwMtF4AWK6l7X7dpkcvhgO5gDj18\nEQfaWq0JoPsqBQDdLKF/l+BJZIHub+TeKx/zQPs2Q+Akw8ncNTfdV4COKRk8NJGypQa6ecYC\ndFg2BDr0MUgCtBms4gTQZgTo5ZPEAW3mgHbvCdBSyejDw7GwJQfaNN/pbdwilEMAbdQCPVxQ\nH2gjDXTvmHgR0KZufutTPND9goWTTA82A7QB6PAS39NdvkU0BTwqaoBusiPQ3l5RoI0OoHur\nkxvQ7jAAvbak9p6UbpFMCY8KQE/2DM4HAt27iX9B5y89UzYCemhXT1+dQLcX+wczAL2kpPac\nkm8RTBGPCkBP9QzOhwM9sqRQoCfWLUOgjfECbayb+YZaDrTxbiKAFimxXkDcsEUuRTwqAD3V\nMzjveQq3tq0Bug/n8YDuFSycpD+Y8W4i38PRVgN0eEl9kHfW1LUAdCTQATfPEGhrST6ge7de\nDnT/8DgXoJ1qgN6/hFHEStQCPb7bR5eEL9S++QjQIwveFujhkiaAHh5gRwFtdgK6d7HvNEAn\nKmEUsRJlQF9jAx2YzIB27tldnivQI2s8BLr55sYBemyoLYDuXQPQKUoYRawEoEcLFq/PGqDb\ne7tXxwPdO70S6JEFZgb0xB0AOkUJo4iVAPRowdIUBnRzz969m4syAXqmBKAVtxQxim6gF2QH\noE0E0L2TckBbF8kDbQBaMKiWYUnqUQB6tGBpgoCeKcsG6CeAtlIEBepaihhFJ9CnHAdoT684\n0P2LR4C+XjAFdO88QIsF1TIsST0KQPsXvujWzX0aoNdnN6B7l/eANgDtpAgK1LUUMYpioJfd\nfPvtXBDQ9p1HgA7oBegELYySYwtAKwE6JAUDPbMu3hsD9P4ljCJWshPQTwXk9un29jb1Spwz\nshZjK3fbv/p2wSynm91a977tLprrXRfRpf1Y1DOU6IveI+iF4Qh66gjavfp0BB36Gr/n57gz\nOoKeK+EIWnFLEaMAtFhOQO8xyuqOGdp6QAdK6HEcoNflIPvBbi1FjALQYgFo6yKAXp6D7Ae7\ntRQxCkCL5cQSQJutgV4agN6/hFHESgBaLPUuLQqA7ncBdFjSbw5dLUWMAtBiAeilSf/AA7Ti\nliJGAWixZA/0TGygDUAHL0Ms6TeHrpYiRgFosRwN6MB7AbRU0m8OXS1FjALQYtEO9LoSgBZL\n+s2hq6WIUQBaLAC9WUlMAHr/EkYRKwFosQD0ZiUxAej9SxhFrASg1bVktrkAWirpN4euliJG\nAWh1LcfZXOlLAFpxSxGjALS6luNsrvQlAK24pYhRAFpdy3E2V/oSgFbcUsQoAK2u5TibK30J\nQCtuKWIUgFbXcpzNlb4EoBW3FDEKQKtrOc7mSl8C0IpbihgFoNW1HGdzpS8BaMUtRYwC0Opa\njrO50pcAtOKWIkYBaHUtx9lc6UsAWnFLEaMAambecwAACVFJREFUtLqW42yu9CUArbiliFEA\nWl3LcTZX+hKAVtxSxCgAra7lOJsrfQlAK24pYhSAVtdynM2VvgSgFbcUMQpAq2s5zuZKXwLQ\niluKGAWg1bUcZ3OlLwFoxS1FjALQ6lqOs7nSlwC04pYiRgFodS3H2VzpSwBacUsRowC0upbj\nbK70JQCtuKWIUQBaXctxNlf6EoBW3FLEKACtruU4myt9CUArbiliFIBW13KczZW+BKAVtxQx\nCkCraznO5kpfAtCKW4oYBaDVtRxnc6UvAWjFLUWMAtDqWo6zudKXALTiliJGAWh1LcfZXOlL\nAFpxSxGjALS6luNsrvQlAK24pYhRAFpdy3E2V/oSgFbcUsQoOwFNSJbhGUryzi5AT2f66EVV\nDjPKYQYRmeQ4W4NRskzIKAAtkMOMcphBANoNo+QYgN4phxnlMIMAtBtGyTEAvVMOM8phBgFo\nN4ySY/IGmhBCyGQAmhBCMg1AE0JIpgFoQgjJNABNCCGZZgegvz7cVdX94+XMl4equnv42l37\nofLdLNMEjvLn26p6+2n3tVuQwEHO11aVyThhk3yvrmmvaS54++H7iqKvL0VvQu+5dRaP4jw/\nB9ssZeJGOeVDbs/WsN1n9Jm7PdDvr9v8/enM4/VM6/Bjs/7OzTJN4Chvr0+yNCsZksBBzrnL\nGujASb6MAm3ffGnRXR6HE0tHcZ6fg22WNFGjnPKY3bM1aIXGn7mbA/21qj69/G34qar+NKe9\n/eG7+f5Q3Vkr5rlZngkc5VP15svLjd9W2R5DBw5yzocqu6e8ldBJPgyeVs01p2PhLwuLrmf+\nrO6yOIZeOIr7/Oxvs7SJGsX0n7tZJGiFxp+5mwP9cN01/qzenHofzmfur1v/Q9Ucnzk3yzSB\no7ypnk9fvmbynPckcJBTvlZZH0GHTnJ/eUysdFN9CHmgnKKHKwjvqw8xKy+VhaM4z8/+Nkuc\nmFFM/7mbR0JWaOKZuznQd836nRrfX4/hHy/fKd5Vb56vK+LcLNMEjmKsW+WZBYO8qbJ+DTp0\nkuFf+9ZU95f7fX9/V909XCE/veL8xvoWyCm6qy5Hzs/VvdgkEVk4inO33jZLnZhRvDth+lxX\n6M/7l4Piy4vML5d8educOWfimbvfpzhOf8vdV5eV+np5Zp8ORPobNN/jzi5Bo3zN+UXoa2YH\n+fRyYXZPeV+mJ/laPXx60+3n52u7qS7HL8931suAj6NvI5yK2vvm8e3eulEuz8/eNkudmFH8\nniTPZYWuL5afj5BfprmcaYWe2Ad3A/q8vSv7OKR/qrtZ5gka5fEuj28apzI7yPPpVdbsnvKe\nzEzy5/CdJ2uq72dn764vMp9eV/5eVR++e99GcIq+57FpVo1yfX56tlnKxIwyWEIeOa/Qp+rt\ny8HB9w/nv0lObzWf53hwbuOc2B/o88tF80C/GbxYmF8CRrmvgt7kSJzZQe5Pr7xm95T3ZGaS\nh+ru9Gg8Nq9NGHeq0+lP193+z9Pryh8u+87X4RHyuejhCv2nPDbNilHa52e+QC8eZbiELHJe\noYa185nqMtRXzw6XDujLc3oW6IdMPu4zlZBR3t6/yeVDWOOZHeTP61/4u6/Z0sxN8ua6C1uv\ntPYpuG/v/Pb0DenI54IvRV/Oj+33T5l8ZGDFKO3zM3Ogl4wyXEIWaVfo6+OHt1egn91rMgD6\n+ir4HNDvFfgcOIr5mvtrHLODfL87P5Oye8oPEvqQvHyTfOe75nTa+gTu+MjN8/P6oehMPnS7\napTr8zNzoJeMMlxCFrms0PN9O0a7ihkB3TyxZ3YhRT4HaPAl73cJ5we5fposu6d8P+EPif+a\n59MDFUJB9/y8vguf3ZuEwaOY6/MzX6AXjzJYQh45r9Dpvc43D5+eMwX6vnliNx9HtT6f5Lxw\nm7/PgaN4z2eVgEGcvSPfrHtIrGv+PL3w4dzSP/Dg+fklu48+hI7SXuXZZikTM8rsjdLkvEIP\np7cFmzNDoCeeuTsA/fymfWK/v34r8sXzWqB1s2wTNEr7TlR2z5UuQYOoAHrRQ/LsPdI6v0L9\n1n5Byvdqp+f5+SGPHxZdOIrz/PRss5SJGWWwhMS5b/Yi067V2BH0hIvbA/1Y3X3tTl/+hrCO\nRZoVsW+Wa8JGeWjfec72E4OBj4nvXGZZ9pB86n7iu5vq0/mFig/XO5+/W/5w2VGsl6ydosaF\nN1VWP+odOIrz/PRss5SJGaW/hNS5vDD+bL/R/jAC9MQ+uDnQz9Wd9cG54U/+t3+33GX/+brA\nUb5e3lR+vBv7KEDyBA7iPZdXlj0k9u8RaKY6/Rqx0+P0/a66f24+U/v9/Eko+5OqTtH76u3L\nXb7c5/GT3ktHcZ+fef4ujlWjOEtIn4fq7Xfz/Pb8JHl7eonjZStXp7/Sh0BP7IM7/C4O+/vk\nT2M/MPCg4NvpwFEy+wVhnoQO4juXV0Inuf6kioVsd8frZ7SaR835vXjP/qLrz4Vl8bLt4lHc\n5+dwm6VM1CjXJey8yqO5/hDk2dzrb1P88Mb+5Iy1quPP3M2B7jb5ufHx/CPpww+W926WZQJH\nufwurrv3+X5HEDyI51xeWfSQvHn/fXjP+/Y3D59+60N1/6W7vf0Q9oo+vamqt3mYtniU3iWD\nbZYycaNclrDXus7m+bxul9Onj/28THF+W9kD9Pgzl39RhRBCMg1AE0JIpgFoQgjJNABNCCGZ\nBqAJISTTADQhhGQagCaEkEwD0IQQkmkAmhw5N3Yu51OvEiHh4elKjhyAJqrD05UcOQBNVIen\nKzl8UJloDc9ccvgANNEanrnk8LGA7l7o+O3VzavfzN+/3Ny8/ny+6u9fqpvq3d+pVpIQTwCa\nHD4+oF+fX5X+R3X+chL64/WF6o/p1pOQfgCaHD5eoL+Z316+vPrr9OW1Md9ubqq/zF8vB9Hf\nEq4pIW4Amhw+PqA/O1+MeXc5dv58c/PvVKtJyCAATQ4f72vQvS+vrrc5H04TkkkAmhw+IUC7\nH5cmJI/wbCSHD0ATreHZSA6fJS9xEJJTeFaSwycE6OubhN94DZrkFIAmh08I0KeP2X02315f\nPthBSB4BaHL4hADd/qDKuzTrSIgvAE0OnyCgzV+/VDc3/+AHCUlOAWhCCMk0AE0IIZkGoAkh\nJNMANCGEZBqAJoSQTAPQhBCSaQCaEEIyDUATQkimAWhCCMk0AE0IIZnm/wEwjpXmIF7qvgAA\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data$dataset <- \"Test\"\n",
    "data$dataset[train_indices] <- \"Train\"\n",
    "data$dataset <- factor(data$dataset, levels = c(\"Train\", \"Test\"), ordered = TRUE)\n",
    "\n",
    "p <- ggplot(data, aes(Time, Demand))\n",
    "p <- p + geom_line(alpha = .5)\n",
    "p <- p + facet_wrap(~ dataset, scales = \"free_x\")\n",
    "p <- p + theme_bw() + theme(\n",
    "    strip.text = element_text(size = 14, face = \"bold\"),\n",
    "    axis.title = element_text(size = 14, face = \"bold\"),\n",
    "    axis.text = element_text(size = 14)\n",
    "    )\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::create_lagged_df(type = \"train\")`\n",
    "\n",
    "* The outcome--`Demand`--and non-dynamic features--`Temperature`--will be lagged to produce additional model features.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 28</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Demand</th><th scope=col>Demand_lag_48</th><th scope=col>Demand_lag_60</th><th scope=col>Demand_lag_72</th><th scope=col>Demand_lag_84</th><th scope=col>Demand_lag_96</th><th scope=col>Demand_lag_108</th><th scope=col>Demand_lag_120</th><th scope=col>Demand_lag_132</th><th scope=col>Demand_lag_144</th><th scope=col>...</th><th scope=col>Temperature_lag_120</th><th scope=col>Temperature_lag_132</th><th scope=col>Temperature_lag_144</th><th scope=col>Temperature_lag_336</th><th scope=col>Temperature_lag_17520</th><th scope=col>Holiday</th><th scope=col>hour</th><th scope=col>weekday</th><th scope=col>month</th><th scope=col>year</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>...</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>17521</th><td>3793.408</td><td>3798.725</td><td>4024.087</td><td>3773.823</td><td>3153.369</td><td>3860.470</td><td>4242.562</td><td>4179.424</td><td>3457.442</td><td>3884.273</td><td>...</td><td>19.4</td><td>15.8</td><td>17.5</td><td>28.3</td><td>21.05</td><td>FALSE</td><td>0</td><td>2</td><td>12</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>17522</th><td>3539.669</td><td>3553.194</td><td>3976.957</td><td>3736.326</td><td>3286.841</td><td>3598.926</td><td>4130.221</td><td>4140.792</td><td>3611.500</td><td>3603.680</td><td>...</td><td>19.7</td><td>16.3</td><td>17.4</td><td>28.3</td><td>20.70</td><td>FALSE</td><td>0</td><td>2</td><td>12</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>17523</th><td>3331.797</td><td>3350.125</td><td>3911.977</td><td>3726.622</td><td>3416.320</td><td>3396.722</td><td>4047.653</td><td>4132.465</td><td>3803.363</td><td>3430.441</td><td>...</td><td>20.6</td><td>16.2</td><td>17.4</td><td>28.1</td><td>20.55</td><td>FALSE</td><td>1</td><td>2</td><td>12</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>17524</th><td>3399.011</td><td>3411.350</td><td>3869.712</td><td>3706.496</td><td>3463.026</td><td>3442.153</td><td>3986.940</td><td>4097.013</td><td>3847.211</td><td>3504.365</td><td>...</td><td>20.0</td><td>16.6</td><td>17.4</td><td>29.0</td><td>20.40</td><td>FALSE</td><td>1</td><td>2</td><td>12</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>17525</th><td>3336.056</td><td>3334.223</td><td>3903.324</td><td>3690.539</td><td>3571.581</td><td>3370.289</td><td>4001.785</td><td>4067.422</td><td>3982.959</td><td>3405.804</td><td>...</td><td>21.2</td><td>16.9</td><td>17.3</td><td>29.4</td><td>20.25</td><td>FALSE</td><td>2</td><td>2</td><td>12</td><td>2012</td></tr>\n",
       "\t<tr><th scope=row>17526</th><td>3204.986</td><td>3193.918</td><td>3963.970</td><td>3696.588</td><td>3693.446</td><td>3231.974</td><td>4036.003</td><td>4069.680</td><td>4105.008</td><td>3274.821</td><td>...</td><td>20.9</td><td>16.1</td><td>16.4</td><td>29.1</td><td>20.10</td><td>FALSE</td><td>2</td><td>2</td><td>12</td><td>2012</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 28\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & Demand & Demand\\_lag\\_48 & Demand\\_lag\\_60 & Demand\\_lag\\_72 & Demand\\_lag\\_84 & Demand\\_lag\\_96 & Demand\\_lag\\_108 & Demand\\_lag\\_120 & Demand\\_lag\\_132 & Demand\\_lag\\_144 & ... & Temperature\\_lag\\_120 & Temperature\\_lag\\_132 & Temperature\\_lag\\_144 & Temperature\\_lag\\_336 & Temperature\\_lag\\_17520 & Holiday & hour & weekday & month & year\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & ... & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <lgl> & <int> & <fct> & <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t17521 & 3793.408 & 3798.725 & 4024.087 & 3773.823 & 3153.369 & 3860.470 & 4242.562 & 4179.424 & 3457.442 & 3884.273 & ... & 19.4 & 15.8 & 17.5 & 28.3 & 21.05 & FALSE & 0 & 2 & 12 & 2012\\\\\n",
       "\t17522 & 3539.669 & 3553.194 & 3976.957 & 3736.326 & 3286.841 & 3598.926 & 4130.221 & 4140.792 & 3611.500 & 3603.680 & ... & 19.7 & 16.3 & 17.4 & 28.3 & 20.70 & FALSE & 0 & 2 & 12 & 2012\\\\\n",
       "\t17523 & 3331.797 & 3350.125 & 3911.977 & 3726.622 & 3416.320 & 3396.722 & 4047.653 & 4132.465 & 3803.363 & 3430.441 & ... & 20.6 & 16.2 & 17.4 & 28.1 & 20.55 & FALSE & 1 & 2 & 12 & 2012\\\\\n",
       "\t17524 & 3399.011 & 3411.350 & 3869.712 & 3706.496 & 3463.026 & 3442.153 & 3986.940 & 4097.013 & 3847.211 & 3504.365 & ... & 20.0 & 16.6 & 17.4 & 29.0 & 20.40 & FALSE & 1 & 2 & 12 & 2012\\\\\n",
       "\t17525 & 3336.056 & 3334.223 & 3903.324 & 3690.539 & 3571.581 & 3370.289 & 4001.785 & 4067.422 & 3982.959 & 3405.804 & ... & 21.2 & 16.9 & 17.3 & 29.4 & 20.25 & FALSE & 2 & 2 & 12 & 2012\\\\\n",
       "\t17526 & 3204.986 & 3193.918 & 3963.970 & 3696.588 & 3693.446 & 3231.974 & 4036.003 & 4069.680 & 4105.008 & 3274.821 & ... & 20.9 & 16.1 & 16.4 & 29.1 & 20.10 & FALSE & 2 & 2 & 12 & 2012\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 28\n",
       "\n",
       "| <!--/--> | Demand &lt;dbl&gt; | Demand_lag_48 &lt;dbl&gt; | Demand_lag_60 &lt;dbl&gt; | Demand_lag_72 &lt;dbl&gt; | Demand_lag_84 &lt;dbl&gt; | Demand_lag_96 &lt;dbl&gt; | Demand_lag_108 &lt;dbl&gt; | Demand_lag_120 &lt;dbl&gt; | Demand_lag_132 &lt;dbl&gt; | Demand_lag_144 &lt;dbl&gt; | ... ... | Temperature_lag_120 &lt;dbl&gt; | Temperature_lag_132 &lt;dbl&gt; | Temperature_lag_144 &lt;dbl&gt; | Temperature_lag_336 &lt;dbl&gt; | Temperature_lag_17520 &lt;dbl&gt; | Holiday &lt;lgl&gt; | hour &lt;int&gt; | weekday &lt;fct&gt; | month &lt;fct&gt; | year &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 17521 | 3793.408 | 3798.725 | 4024.087 | 3773.823 | 3153.369 | 3860.470 | 4242.562 | 4179.424 | 3457.442 | 3884.273 | ... | 19.4 | 15.8 | 17.5 | 28.3 | 21.05 | FALSE | 0 | 2 | 12 | 2012 |\n",
       "| 17522 | 3539.669 | 3553.194 | 3976.957 | 3736.326 | 3286.841 | 3598.926 | 4130.221 | 4140.792 | 3611.500 | 3603.680 | ... | 19.7 | 16.3 | 17.4 | 28.3 | 20.70 | FALSE | 0 | 2 | 12 | 2012 |\n",
       "| 17523 | 3331.797 | 3350.125 | 3911.977 | 3726.622 | 3416.320 | 3396.722 | 4047.653 | 4132.465 | 3803.363 | 3430.441 | ... | 20.6 | 16.2 | 17.4 | 28.1 | 20.55 | FALSE | 1 | 2 | 12 | 2012 |\n",
       "| 17524 | 3399.011 | 3411.350 | 3869.712 | 3706.496 | 3463.026 | 3442.153 | 3986.940 | 4097.013 | 3847.211 | 3504.365 | ... | 20.0 | 16.6 | 17.4 | 29.0 | 20.40 | FALSE | 1 | 2 | 12 | 2012 |\n",
       "| 17525 | 3336.056 | 3334.223 | 3903.324 | 3690.539 | 3571.581 | 3370.289 | 4001.785 | 4067.422 | 3982.959 | 3405.804 | ... | 21.2 | 16.9 | 17.3 | 29.4 | 20.25 | FALSE | 2 | 2 | 12 | 2012 |\n",
       "| 17526 | 3204.986 | 3193.918 | 3963.970 | 3696.588 | 3693.446 | 3231.974 | 4036.003 | 4069.680 | 4105.008 | 3274.821 | ... | 20.9 | 16.1 | 16.4 | 29.1 | 20.10 | FALSE | 2 | 2 | 12 | 2012 |\n",
       "\n"
      ],
      "text/plain": [
       "      Demand   Demand_lag_48 Demand_lag_60 Demand_lag_72 Demand_lag_84\n",
       "17521 3793.408 3798.725      4024.087      3773.823      3153.369     \n",
       "17522 3539.669 3553.194      3976.957      3736.326      3286.841     \n",
       "17523 3331.797 3350.125      3911.977      3726.622      3416.320     \n",
       "17524 3399.011 3411.350      3869.712      3706.496      3463.026     \n",
       "17525 3336.056 3334.223      3903.324      3690.539      3571.581     \n",
       "17526 3204.986 3193.918      3963.970      3696.588      3693.446     \n",
       "      Demand_lag_96 Demand_lag_108 Demand_lag_120 Demand_lag_132 Demand_lag_144\n",
       "17521 3860.470      4242.562       4179.424       3457.442       3884.273      \n",
       "17522 3598.926      4130.221       4140.792       3611.500       3603.680      \n",
       "17523 3396.722      4047.653       4132.465       3803.363       3430.441      \n",
       "17524 3442.153      3986.940       4097.013       3847.211       3504.365      \n",
       "17525 3370.289      4001.785       4067.422       3982.959       3405.804      \n",
       "17526 3231.974      4036.003       4069.680       4105.008       3274.821      \n",
       "      ... Temperature_lag_120 Temperature_lag_132 Temperature_lag_144\n",
       "17521 ... 19.4                15.8                17.5               \n",
       "17522 ... 19.7                16.3                17.4               \n",
       "17523 ... 20.6                16.2                17.4               \n",
       "17524 ... 20.0                16.6                17.4               \n",
       "17525 ... 21.2                16.9                17.3               \n",
       "17526 ... 20.9                16.1                16.4               \n",
       "      Temperature_lag_336 Temperature_lag_17520 Holiday hour weekday month year\n",
       "17521 28.3                21.05                 FALSE   0    2       12    2012\n",
       "17522 28.3                20.70                 FALSE   0    2       12    2012\n",
       "17523 28.1                20.55                 FALSE   1    2       12    2012\n",
       "17524 29.0                20.40                 FALSE   1    2       12    2012\n",
       "17525 29.4                20.25                 FALSE   2    2       12    2012\n",
       "17526 29.1                20.10                 FALSE   2    2       12    2012"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The column position of our 'Demand' outcome (after removing the date columns).\n",
    "outcome_col <- 1\n",
    "\n",
    "# Forecast 1, 1:2, and 1:3 days into the future in 30-second increments; horizons: c(48, 96, 144).\n",
    "horizons <- c(records_per_day, records_per_day * 2, records_per_day * 3)\n",
    "\n",
    "# Feature lags in 30 minute intervals: c(48, 60, 72, 84, 96, 108, 120, 132, 144, 336, 17520).\n",
    "# These will be the same across the 3 horizon-specific models and lagged features but can \n",
    "# easily be customized. Notice that feature lags that do not support direct forecasting at \n",
    "# a given horizon are silently dropped.\n",
    "lookback <- c(seq(48, records_per_day * 3, 12), records_per_day * 7, records_per_day * 365)\n",
    "\n",
    "dates <- train$Time\n",
    "\n",
    "# We don't need or want dates/times in the modeling dataset.\n",
    "train$Time <- NULL\n",
    "train$Date <- NULL\n",
    "\n",
    "# Features that change through time but which will not be lagged.\n",
    "dynamic_features <- c(\"Holiday\", \"hour\", \"weekday\", \"month\", \"year\")\n",
    "\n",
    "data_train <- forecastML::create_lagged_df(train, type = \"train\", outcome_col = outcome_col,\n",
    "                                           lookback = lookback, horizon = horizons,\n",
    "                                           dates = dates, frequency = frequency,\n",
    "                                           dynamic_features = dynamic_features\n",
    "                                           )\n",
    "\n",
    "head(data_train$horizon_48)  # View the horizon-48 dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optional - External validation datasets with `forecastML::create_windows()`\n",
    "\n",
    "* The \"optional\" part is that you could set `create_windows(window_length = 0)` and train a model over all of the training data and not worry about assessing historical forecast performance; this--no external CV--is how the final model is trained.\n",
    "  \n",
    "  \n",
    "* We'll measure our models' generalization performance on 1 validation window. This window is a similar time of the year as our test dataset--December--but 1 year in the past.\n",
    "  \n",
    "  \n",
    "* You can have multiple validation windows; though, 1 model will be trained for each contiguous validation window so the challenge will be in choosing the optimal hyperparameters for the final model...or use a bunch of models trained on different data or differentially weighted data. The choice is yours.\n",
    "  \n",
    "  \n",
    "* Notice how the first year of data is missing in the plot below. This is because our longest feature lookback was 1 year in the past which would have introduced missing data for these features at any time in 2012 (if the dataset rows were retained). These rows can be kept with `create_lagged_df(keep_rows = TRUE)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yaTTnJ4IWpEQWf7oT3K9oo8msx4OEHLDaK0x6eUuuiCFq398TqhNxO0J+9Vvkl4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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "windows <- forecastML::create_windows(data_train,\n",
    "                                      window_length = 0,  # 0 spans from window_start to window_stop.\n",
    "                                      window_start = as.POSIXct(\"2013-12-01\", tz = \"UTC\"),\n",
    "                                      window_stop = as.POSIXct(\"2014-01-01\", tz = \"UTC\")\n",
    "                                     )\n",
    "\n",
    "plot(windows, data_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "## Modeling in `forecastML`\n",
    "\n",
    "* **`Python` workflow**:\n",
    "    1. Read a .py script with `reticulate` in `R` to import `Python` libraries, classes, and functions. For non-parallel training, a `Python` code block in `R` Markdown works.\n",
    "    2. Write an `R` wrapper. For non-parallel training, this is optional. The purpose of the `R` wrapper is to save a pickeled trained `Python` model to disk because the pointers that `R` uses to find the correct `Python` object are ephemeral and the models will be lost when training in parallel.\n",
    "    3. Load the saved pickeled model into `R` with `reticulate` and attach it as an attribute in the \"model\" slot of a `forecastML` trained model object."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `Python` model function\n",
    "#### `Python` model function in `model_script.py`\n",
    "\n",
    "* The two cells below are plain text but illustrate the function used in `model_script.py` which is in the same directory as this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'\\nimport pandas as pd\\nfrom sklearn import linear_model\\nfrom sklearn.preprocessing import StandardScaler\\n'"
      ],
      "text/latex": [
       "'\\textbackslash{}nimport pandas as pd\\textbackslash{}nfrom sklearn import linear\\_model\\textbackslash{}nfrom sklearn.preprocessing import StandardScaler\\textbackslash{}n'"
      ],
      "text/markdown": [
       "'\\nimport pandas as pd\\nfrom sklearn import linear_model\\nfrom sklearn.preprocessing import StandardScaler\\n'"
      ],
      "text/plain": [
       "[1] \"\\nimport pandas as pd\\nfrom sklearn import linear_model\\nfrom sklearn.preprocessing import StandardScaler\\n\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\n",
    "import pandas as pd\n",
    "from sklearn import linear_model\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'\\n# \\'data\\' is a pd.DataFrame version of the horizon-specific data.frame from \\n# create_lagged_df(). The pd.DataFrame is not subclassed.\\ndef py_model_fun(data):\\n  \\n  # A special attribute to identify the direct forecast horizon for \\'data\\': 48, 96, and 144 here.\\n  # Using a setup like \\'if horizon == 48: \\'my neural network code\\'\\' would allow you to train \\n  # entirely different models at each direct forecast horizon.\\n  horizon = int(data.horizons)\\n  \\n  X = data.iloc[:, 1:]\\n  y = data.iloc[:, 0]\\n  \\n  scaler = StandardScaler()\\n  X = scaler.fit_transform(X)\\n  \\n  model_lasso = linear_model.LassoCV(cv = 5)\\n  \\n  model_lasso.fit(X = X, y = y)\\n  \\n  # The returned object has no real restrictions. Here, we\\'re returning meta-data from \\n  # hyperparameters as well as the forecast \\'horizon\\' which we\\'ll use to uniquely name \\n  # the .pkl files that we\\'re saving to disk.\\n  return({\\'model\\': model_lasso, \\'scaler\\': scaler, \\'horizon\\': horizon})\\n}\\n'</span>"
      ],
      "text/latex": [
       "'\\textbackslash{}n\\# \\textbackslash{}'data\\textbackslash{}' is a pd.DataFrame version of the horizon-specific data.frame from \\textbackslash{}n\\# create\\_lagged\\_df(). The pd.DataFrame is not subclassed.\\textbackslash{}ndef py\\_model\\_fun(data):\\textbackslash{}n  \\textbackslash{}n  \\# A special attribute to identify the direct forecast horizon for \\textbackslash{}'data\\textbackslash{}': 48, 96, and 144 here.\\textbackslash{}n  \\# Using a setup like \\textbackslash{}'if horizon == 48: \\textbackslash{}'my neural network code\\textbackslash{}'\\textbackslash{}' would allow you to train \\textbackslash{}n  \\# entirely different models at each direct forecast horizon.\\textbackslash{}n  horizon = int(data.horizons)\\textbackslash{}n  \\textbackslash{}n  X = data.iloc{[}:, 1:{]}\\textbackslash{}n  y = data.iloc{[}:, 0{]}\\textbackslash{}n  \\textbackslash{}n  scaler = StandardScaler()\\textbackslash{}n  X = scaler.fit\\_transform(X)\\textbackslash{}n  \\textbackslash{}n  model\\_lasso = linear\\_model.LassoCV(cv = 5)\\textbackslash{}n  \\textbackslash{}n  model\\_lasso.fit(X = X, y = y)\\textbackslash{}n  \\textbackslash{}n  \\# The returned object has no real restrictions. Here, we\\textbackslash{}'re returning meta-data from \\textbackslash{}n  \\# hyperparameters as well as the forecast \\textbackslash{}'horizon\\textbackslash{}' which we\\textbackslash{}'ll use to uniquely name \\textbackslash{}n  \\# the .pkl files that we\\textbackslash{}'re saving to disk.\\textbackslash{}n  return(\\{\\textbackslash{}'model\\textbackslash{}': model\\_lasso, \\textbackslash{}'scaler\\textbackslash{}': scaler, \\textbackslash{}'horizon\\textbackslash{}': horizon\\})\\textbackslash{}n\\}\\textbackslash{}n'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'\\n# \\'data\\' is a pd.DataFrame version of the horizon-specific data.frame from \\n# create_lagged_df(). The pd.DataFrame is not subclassed.\\ndef py_model_fun(data):\\n  \\n  # A special attribute to identify the direct forecast horizon for \\'data\\': 48, 96, and 144 here.\\n  # Using a setup like \\'if horizon == 48: \\'my neural network code\\'\\' would allow you to train \\n  # entirely different models at each direct forecast horizon.\\n  horizon = int(data.horizons)\\n  \\n  X = data.iloc[:, 1:]\\n  y = data.iloc[:, 0]\\n  \\n  scaler = StandardScaler()\\n  X = scaler.fit_transform(X)\\n  \\n  model_lasso = linear_model.LassoCV(cv = 5)\\n  \\n  model_lasso.fit(X = X, y = y)\\n  \\n  # The returned object has no real restrictions. Here, we\\'re returning meta-data from \\n  # hyperparameters as well as the forecast \\'horizon\\' which we\\'ll use to uniquely name \\n  # the .pkl files that we\\'re saving to disk.\\n  return({\\'model\\': model_lasso, \\'scaler\\': scaler, \\'horizon\\': horizon})\\n}\\n'</span>"
      ],
      "text/plain": [
       "[1] \"\\n# 'data' is a pd.DataFrame version of the horizon-specific data.frame from \\n# create_lagged_df(). The pd.DataFrame is not subclassed.\\ndef py_model_fun(data):\\n  \\n  # A special attribute to identify the direct forecast horizon for 'data': 48, 96, and 144 here.\\n  # Using a setup like 'if horizon == 48: 'my neural network code'' would allow you to train \\n  # entirely different models at each direct forecast horizon.\\n  horizon = int(data.horizons)\\n  \\n  X = data.iloc[:, 1:]\\n  y = data.iloc[:, 0]\\n  \\n  scaler = StandardScaler()\\n  X = scaler.fit_transform(X)\\n  \\n  model_lasso = linear_model.LassoCV(cv = 5)\\n  \\n  model_lasso.fit(X = X, y = y)\\n  \\n  # The returned object has no real restrictions. Here, we're returning meta-data from \\n  # hyperparameters as well as the forecast 'horizon' which we'll use to uniquely name \\n  # the .pkl files that we're saving to disk.\\n  return({'model': model_lasso, 'scaler': scaler, 'horizon': horizon})\\n}\\n\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\n",
    "# 'data' is a pd.DataFrame version of the horizon-specific data.frame from \n",
    "# create_lagged_df(). The pd.DataFrame is not subclassed.\n",
    "def py_model_fun(data):\n",
    "  \n",
    "  # A special attribute to identify the direct forecast horizon for 'data': 48, 96, and 144 here.\n",
    "  # Using a setup like 'if horizon == 48: 'my neural network code'' would allow you to train \n",
    "  # entirely different models at each direct forecast horizon.\n",
    "  horizon = int(data.horizons)\n",
    "  \n",
    "  X = data.iloc[:, 1:]\n",
    "  y = data.iloc[:, 0]\n",
    "  \n",
    "  scaler = StandardScaler()\n",
    "  X = scaler.fit_transform(X)\n",
    "  \n",
    "  model_lasso = linear_model.LassoCV(cv = 5)\n",
    "  \n",
    "  model_lasso.fit(X = X, y = y)\n",
    "  \n",
    "  # The returned object has no real restrictions. Here, we're returning meta-data from \n",
    "  # hyperparameters as well as the forecast 'horizon' which we'll use to uniquely name \n",
    "  # the .pkl files that we're saving to disk.\n",
    "  return({'model': model_lasso, 'scaler': scaler, 'horizon': horizon})\n",
    "}\n",
    "\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `R` wrapper for `Python` model function in `model_script.py`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 'data' is a pd.DataFrame version of the horizon-specific data.frame from \n",
    "# create_lagged_df(). The pd.DataFrame is not subclassed.\n",
    "r_wrapper_for_py_model_fun <- function(data) {\n",
    "  \n",
    "  reticulate::source_python(\"model_script.py\")\n",
    "  \n",
    "  py_model_return <- reticulate::py$py_model_fun(data)  # py$ brings the function into R.\n",
    "  \n",
    "  horizon <- py_model_return$horizon  # This is our dict key 'horizon' in the cell above.\n",
    "  \n",
    "  # A uniquely named Python model object with meta-data being saved to disk for parallel training.\n",
    "  reticulate::py_save_object(py_model_return, paste0(\"py_model_horizon_\", horizon, \".pkl\"), \n",
    "                             pickle = \"pickle\")\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `R` model function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_model_fun <- function(data) {\n",
    "\n",
    "  outcome_names <- names(data)[1]\n",
    "  model_formula <- formula(paste0(outcome_names,  \"~ .\"))\n",
    "\n",
    "  model <- ranger::ranger(model_formula, data = data, num.trees = 300)\n",
    "  return(model)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::train_model()`\n",
    "\n",
    "#### `Python` - Model training with internal and external CV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "future::plan(future::multiprocess)  # Mutli-core on Linux; multi-R-session on Windows.\n",
    "\n",
    "model_results_py <- forecastML::train_model(data_train,\n",
    "                                            windows = windows,\n",
    "                                            model_name = \"Python LASSO\",  # Can be any name.\n",
    "                                            model_function = r_wrapper_for_py_model_fun,\n",
    "                                            use_future = TRUE,  # Parallel training.\n",
    "                                            python = TRUE\n",
    "                                            )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* This is step 3 from the `Python` workflow mentioned earlier. At present, this is a bit manual due to obstacles when using `reticulate` in parallel.\n",
    "  \n",
    "  \n",
    "* The `Python` model is now where it needs to be. If you trained with multiple validation windows, you'd need a nested loop to assign each model to the correct combination of horizon and window."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "$model\n",
       "LassoCV(alphas=None, copy_X=True, cv=5, eps=0.001, fit_intercept=True,\n",
       "        max_iter=1000, n_alphas=100, n_jobs=None, normalize=False,\n",
       "        positive=False, precompute='auto', random_state=None,\n",
       "        selection='cyclic', tol=0.0001, verbose=False)\n",
       "\n",
       "$scaler\n",
       "StandardScaler(copy=True, with_mean=True, with_std=True)\n",
       "\n",
       "$horizon\n",
       "[1] 144\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for (i in seq_along(horizons)) {\n",
    "  \n",
    "  model_name <- paste0(\"py_model_horizon_\", horizons[i])  # Horizons 48, 96, and 144.\n",
    "  \n",
    "  model_results_py[[i]]$window_1$model <- reticulate::py_load_object(paste0(model_name, \".pkl\"), \n",
    "                                                                     pickle = \"pickle\")\n",
    "}\n",
    "\n",
    "model_results_py[[i]]$window_1$model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `R` - Model training with internal and external CV\n",
    "\n",
    "* There's actually no internal CV in our `R` model function; the hyperparamters are fixed to speed up the runtime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "future::plan(future::multiprocess)  # Mutli-core on Linux; multi-R-session on Windows.\n",
    "\n",
    "model_results_r <- forecastML::train_model(data_train,\n",
    "                                           windows = windows,\n",
    "                                           model_name = \"R Random Forest\",  # Can be any name.\n",
    "                                           model_function = r_model_fun,\n",
    "                                           use_future = TRUE  # Parallel training.\n",
    "                                           )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "## Historical Prediction in Validation Window(s)\n",
    "\n",
    "### `Python` predict function\n",
    "\n",
    "#### `Python` predict function in `model_script.py`\n",
    "\n",
    "* The cell below is plain text but illustrates the function used in `model_script.py`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'\\n# The R model_list list in the wrapper in the next cell will be passed as a Python \\n# dict here: \\'model_dict\\'. \\'data\\' is passed as a pd.DataFrame with the outcome column \\n# removed and a \\'.horizon\\' attribute if needed.\\ndef py_predict_fun(model_dict, data):\\n  \\n  data = model_dict[\\'scaler\\'].transform(data)\\n  \\n  data_pred = pd.DataFrame({\\'y_pred\\': model_dict[\\'model\\'].predict(data)})\\n  \\n  return(data_pred)\\n}\\n'</span>"
      ],
      "text/latex": [
       "'\\textbackslash{}n\\# The R model\\_list list in the wrapper in the next cell will be passed as a Python \\textbackslash{}n\\# dict here: \\textbackslash{}'model\\_dict\\textbackslash{}'. \\textbackslash{}'data\\textbackslash{}' is passed as a pd.DataFrame with the outcome column \\textbackslash{}n\\# removed and a \\textbackslash{}'.horizon\\textbackslash{}' attribute if needed.\\textbackslash{}ndef py\\_predict\\_fun(model\\_dict, data):\\textbackslash{}n  \\textbackslash{}n  data = model\\_dict{[}\\textbackslash{}'scaler\\textbackslash{}'{]}.transform(data)\\textbackslash{}n  \\textbackslash{}n  data\\_pred = pd.DataFrame(\\{\\textbackslash{}'y\\_pred\\textbackslash{}': model\\_dict{[}\\textbackslash{}'model\\textbackslash{}'{]}.predict(data)\\})\\textbackslash{}n  \\textbackslash{}n  return(data\\_pred)\\textbackslash{}n\\}\\textbackslash{}n'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'\\n# The R model_list list in the wrapper in the next cell will be passed as a Python \\n# dict here: \\'model_dict\\'. \\'data\\' is passed as a pd.DataFrame with the outcome column \\n# removed and a \\'.horizon\\' attribute if needed.\\ndef py_predict_fun(model_dict, data):\\n  \\n  data = model_dict[\\'scaler\\'].transform(data)\\n  \\n  data_pred = pd.DataFrame({\\'y_pred\\': model_dict[\\'model\\'].predict(data)})\\n  \\n  return(data_pred)\\n}\\n'</span>"
      ],
      "text/plain": [
       "[1] \"\\n# The R model_list list in the wrapper in the next cell will be passed as a Python \\n# dict here: 'model_dict'. 'data' is passed as a pd.DataFrame with the outcome column \\n# removed and a '.horizon' attribute if needed.\\ndef py_predict_fun(model_dict, data):\\n  \\n  data = model_dict['scaler'].transform(data)\\n  \\n  data_pred = pd.DataFrame({'y_pred': model_dict['model'].predict(data)})\\n  \\n  return(data_pred)\\n}\\n\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\n",
    "# The R model_list list in the wrapper in the next cell will be passed as a Python \n",
    "# dict here: 'model_dict'. 'data' is passed as a pd.DataFrame with the outcome column \n",
    "# removed and a '.horizon' attribute if needed.\n",
    "def py_predict_fun(model_dict, data):\n",
    "  \n",
    "  data = model_dict['scaler'].transform(data)\n",
    "  \n",
    "  data_pred = pd.DataFrame({'y_pred': model_dict['model'].predict(data)})\n",
    "  \n",
    "  return(data_pred)\n",
    "}\n",
    "\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `R` wrapper for `Python` predict function in `model_script.py`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_wrapper_for_py_predict_fun <- function(model_list, data) {\n",
    "  \n",
    "  reticulate::source_python(\"model_script.py\")\n",
    "  \n",
    "  reticulate::py$py_predict_fun(model_list, data)  # py$ brings the function into R.\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `R` predict function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_predict_fun <- function(model, data) {\n",
    "\n",
    "  data_pred <- data.frame(\"y_pred\" = predict(model, data)$predictions)\n",
    "  return(data_pred)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::predict()`\n",
    "\n",
    "* These predictions are for our 1 validation dataset in December 2013."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_valid <- predict(model_results_py, model_results_r,\n",
    "                      prediction_function = list(r_wrapper_for_py_predict_fun, r_predict_fun),\n",
    "                      data = data_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot historical predictions in the validation window\n",
    "\n",
    "* **1st plot:** All ML models, all direct horizons, all 30-minute periods in the validation window.\n",
    "  \n",
    "  \n",
    "* **2nd plot:** 1st plot filtered to focus on December 31st.\n",
    "  \n",
    "  \n",
    "* **3rd plot:** 2nd plot, faceted to plot overlapped models, custom colors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0NG/yYk+y1BulIuGO2aATppugG+fqKA0KoW0OIPU8SXamMGAU5ZQmEo5pWxGB9y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\n7x1rRSx4RH2kmcsBWqGniQXmRr89pNDTeqgjffO0BAJaOpUSU2U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FQDc4LSoDut+OJ+lLvuyGT/QYoJWBRD3h/ruOgOYb89MArdTTJQBd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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KwnAtoqCdCBXUoL0KuHQs9L4FQygEdv4X1qJy+g67wj65TC59aKQcEiXz0R0FYt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\nKA0+45dhSQ8oQAcSOjH7dQHoo9cTS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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UGbDH1E0dn3T0OF0gdwbAXw+LnJAYr8c+dD0Cr9+l8vX99unykhaNOhwgOGzr1/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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1st plot.\n",
    "plot(data_valid)\n",
    "\n",
    "view_dates <- seq(as.POSIXct(\"2013-12-31\", tz = \"UTC\"), \n",
    "                  as.POSIXct(\"2014-01-01\", tz = \"UTC\"), \n",
    "                  by = \"30 min\")\n",
    "\n",
    "# 2nd plot.\n",
    "plot(data_valid, valid_indices = view_dates) + theme(axis.text.x = element_text(angle = 45, hjust = 1)) +\n",
    "  ggtitle(\"1- to 3-Day Out Forecasts: Every 30 Minutes December 31st, 2013\")\n",
    "\n",
    "# 3rd plot.\n",
    "plot(data_valid, facet = horizon ~ ., valid_indices = view_dates) + \n",
    "  ggtitle(\"1- to 3-Day Out Forecasts: Every 30 Minutes December 31st, 2013\") + \n",
    "  scale_color_manual(values = c(\"Python LASSO\" = \"#ffd43b\", \"R Random Forest\" = \"#276DC2\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "## Historical Error in Validation Window(s)\n",
    "\n",
    "### `forecastML::return_error()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_error <- forecastML::return_error(data_valid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `forecastML::plot()` error by direct forecast horizon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ccQKGhhFHQ7FHSoXnD2zh9wDIGCFkZB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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data_error, type = \"horizon\", facet = ~ horizon) + \n",
    "  scale_fill_manual(values = c(\"Python LASSO\" = \"#ffd43b\", \"R Random Forest\" = \"#276DC2\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `forecastML::plot()` error collapsed across direct forecast horizons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Scale for 'fill' is already present. Adding another scale for 'fill', which\n",
      "will replace the existing scale.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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3p4BPrms9h+y2SRJ78PMDrUPc+N+/GSl+t7D0CgoWaaRHZDEMi3Hi6BvvrjdEoX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\nAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data_error, type = \"global\", facet = ~ horizon) + \n",
    "  scale_fill_manual(values = c(\"Python LASSO\" = \"#ffd43b\", \"R Random Forest\" = \"#276DC2\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "## Forecast in `forecastML`\n",
    "\n",
    "### `forecastML::create_lagged_df(type = \"forecast\")`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 13</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>index</th><th scope=col>horizon</th><th scope=col>Demand_lag_144</th><th scope=col>Demand_lag_336</th><th scope=col>Demand_lag_17520</th><th scope=col>Temperature_lag_144</th><th scope=col>Temperature_lag_336</th><th scope=col>Temperature_lag_17520</th><th scope=col>Holiday</th><th scope=col>hour</th><th scope=col>weekday</th><th scope=col>month</th><th scope=col>year</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dttm&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;lgl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>2014-12-29 00:00:00</td><td>1</td><td>3907.916</td><td>4349.082</td><td>3997.274</td><td>11.9</td><td>20.0</td><td>15.9</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>2014-12-29 00:30:00</td><td>2</td><td>3708.430</td><td>4088.169</td><td>3698.171</td><td>13.0</td><td>19.4</td><td>16.1</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>2014-12-29 01:00:00</td><td>3</td><td>3571.791</td><td>3878.761</td><td>3426.123</td><td>13.4</td><td>19.0</td><td>16.0</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>2014-12-29 01:30:00</td><td>4</td><td>3427.215</td><td>3729.914</td><td>3295.835</td><td>13.5</td><td>19.0</td><td>15.6</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>2014-12-29 02:00:00</td><td>5</td><td>3288.186</td><td>3592.806</td><td>3166.052</td><td>13.3</td><td>18.9</td><td>15.4</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>2014-12-29 02:30:00</td><td>6</td><td>3151.568</td><td>3493.213</td><td>3071.107</td><td>12.9</td><td>18.8</td><td>15.4</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 13\n",
       "\\begin{tabular}{r|lllllllllllll}\n",
       "  & index & horizon & Demand\\_lag\\_144 & Demand\\_lag\\_336 & Demand\\_lag\\_17520 & Temperature\\_lag\\_144 & Temperature\\_lag\\_336 & Temperature\\_lag\\_17520 & Holiday & hour & weekday & month & year\\\\\n",
       "  & <dttm> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <lgl> & <lgl> & <lgl> & <lgl> & <lgl>\\\\\n",
       "\\hline\n",
       "\t1 & 2014-12-29 00:00:00 & 1 & 3907.916 & 4349.082 & 3997.274 & 11.9 & 20.0 & 15.9 & NA & NA & NA & NA & NA\\\\\n",
       "\t2 & 2014-12-29 00:30:00 & 2 & 3708.430 & 4088.169 & 3698.171 & 13.0 & 19.4 & 16.1 & NA & NA & NA & NA & NA\\\\\n",
       "\t3 & 2014-12-29 01:00:00 & 3 & 3571.791 & 3878.761 & 3426.123 & 13.4 & 19.0 & 16.0 & NA & NA & NA & NA & NA\\\\\n",
       "\t4 & 2014-12-29 01:30:00 & 4 & 3427.215 & 3729.914 & 3295.835 & 13.5 & 19.0 & 15.6 & NA & NA & NA & NA & NA\\\\\n",
       "\t5 & 2014-12-29 02:00:00 & 5 & 3288.186 & 3592.806 & 3166.052 & 13.3 & 18.9 & 15.4 & NA & NA & NA & NA & NA\\\\\n",
       "\t6 & 2014-12-29 02:30:00 & 6 & 3151.568 & 3493.213 & 3071.107 & 12.9 & 18.8 & 15.4 & NA & NA & NA & NA & NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 13\n",
       "\n",
       "| <!--/--> | index &lt;dttm&gt; | horizon &lt;dbl&gt; | Demand_lag_144 &lt;dbl&gt; | Demand_lag_336 &lt;dbl&gt; | Demand_lag_17520 &lt;dbl&gt; | Temperature_lag_144 &lt;dbl&gt; | Temperature_lag_336 &lt;dbl&gt; | Temperature_lag_17520 &lt;dbl&gt; | Holiday &lt;lgl&gt; | hour &lt;lgl&gt; | weekday &lt;lgl&gt; | month &lt;lgl&gt; | year &lt;lgl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 2014-12-29 00:00:00 | 1 | 3907.916 | 4349.082 | 3997.274 | 11.9 | 20.0 | 15.9 | NA | NA | NA | NA | NA |\n",
       "| 2 | 2014-12-29 00:30:00 | 2 | 3708.430 | 4088.169 | 3698.171 | 13.0 | 19.4 | 16.1 | NA | NA | NA | NA | NA |\n",
       "| 3 | 2014-12-29 01:00:00 | 3 | 3571.791 | 3878.761 | 3426.123 | 13.4 | 19.0 | 16.0 | NA | NA | NA | NA | NA |\n",
       "| 4 | 2014-12-29 01:30:00 | 4 | 3427.215 | 3729.914 | 3295.835 | 13.5 | 19.0 | 15.6 | NA | NA | NA | NA | NA |\n",
       "| 5 | 2014-12-29 02:00:00 | 5 | 3288.186 | 3592.806 | 3166.052 | 13.3 | 18.9 | 15.4 | NA | NA | NA | NA | NA |\n",
       "| 6 | 2014-12-29 02:30:00 | 6 | 3151.568 | 3493.213 | 3071.107 | 12.9 | 18.8 | 15.4 | NA | NA | NA | NA | NA |\n",
       "\n"
      ],
      "text/plain": [
       "  index               horizon Demand_lag_144 Demand_lag_336 Demand_lag_17520\n",
       "1 2014-12-29 00:00:00 1       3907.916       4349.082       3997.274        \n",
       "2 2014-12-29 00:30:00 2       3708.430       4088.169       3698.171        \n",
       "3 2014-12-29 01:00:00 3       3571.791       3878.761       3426.123        \n",
       "4 2014-12-29 01:30:00 4       3427.215       3729.914       3295.835        \n",
       "5 2014-12-29 02:00:00 5       3288.186       3592.806       3166.052        \n",
       "6 2014-12-29 02:30:00 6       3151.568       3493.213       3071.107        \n",
       "  Temperature_lag_144 Temperature_lag_336 Temperature_lag_17520 Holiday hour\n",
       "1 11.9                20.0                15.9                  NA      NA  \n",
       "2 13.0                19.4                16.1                  NA      NA  \n",
       "3 13.4                19.0                16.0                  NA      NA  \n",
       "4 13.5                19.0                15.6                  NA      NA  \n",
       "5 13.3                18.9                15.4                  NA      NA  \n",
       "6 12.9                18.8                15.4                  NA      NA  \n",
       "  weekday month year\n",
       "1 NA      NA    NA  \n",
       "2 NA      NA    NA  \n",
       "3 NA      NA    NA  \n",
       "4 NA      NA    NA  \n",
       "5 NA      NA    NA  \n",
       "6 NA      NA    NA  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_forecast <- forecastML::create_lagged_df(train, type = \"forecast\", outcome_col = 1,\n",
    "                                              lookback = lookback, horizon = horizons,\n",
    "                                              dates = dates, frequency = frequency,\n",
    "                                              dynamic_features = dynamic_features)\n",
    "\n",
    "head(data_forecast$horizon_144)  # View the horizon-144 dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fill in future dynamic features\n",
    "\n",
    "* Filling in future `NA` values for non-lagged features is a bit of a manual process.\n",
    "  \n",
    "  \n",
    "* The features can remain `NA` if the ML model can handle missing values.\n",
    "  \n",
    "  \n",
    "* The feature types (e.g., factor) should match the training dataset to work with the trained ML model. Don't add new features here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loop over the 48-, 96, and 144-step-ahead horizon datasets from create_lagged_df().\n",
    "for (i in seq_along(horizons)) {\n",
    "  \n",
    "  data_forecast[[i]]$hour <- lubridate::hour(data_forecast[[i]]$index)\n",
    "  data_forecast[[i]]$weekday <- factor(lubridate::wday(data_forecast[[i]]$index))\n",
    "  data_forecast[[i]]$month <- factor(lubridate::month(data_forecast[[i]]$index))\n",
    "  data_forecast[[i]]$year <- lubridate::year(data_forecast[[i]]$index)\n",
    "  \n",
    "  # New Year's Eve; this isn't a production-ready approach.\n",
    "  data_forecast[[i]]$Holiday <- with(data_forecast[[i]], \n",
    "                                     ifelse(lubridate::mday(data_forecast[[i]]$index) == 31, \n",
    "                                            TRUE, FALSE))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forecast with `forecastML::predict()`\n",
    "\n",
    "* Unless a new function is needed, the same `predict()` function used to make historical validation predictions can often be used to produce forecasts.\n",
    "  \n",
    "  \n",
    "* We're going to run `predict()` 3 times to view the forecasts at different levels:\n",
    "    1. **`Python` only**\n",
    "    2. **`R` only**\n",
    "    3. **`Python` and `R` together** which will allow is to create a simple ensemble model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_forecasts_py <- predict(model_results_py,\n",
    "                             prediction_function = list(r_wrapper_for_py_predict_fun), \n",
    "                             data = data_forecast)\n",
    "\n",
    "data_forecasts_r <- predict(model_results_r,\n",
    "                            prediction_function = list(r_predict_fun), \n",
    "                            data = data_forecast)\n",
    "\n",
    "data_forecasts <- predict(model_results_py, model_results_r,\n",
    "                          prediction_function = list(r_wrapper_for_py_predict_fun, r_predict_fun), \n",
    "                          data = data_forecast)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `forecastML::plot()` forecasts from the end of the training data\n",
    "\n",
    "* We've purposefully held out a test dataset that matches our 3-day forecast horizon from the end of the training data. This isn't necessary but is good practice. It's the gray line in the plot below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Scale for 'colour' is already present. Adding another scale for 'colour',\n",
      "which will replace the existing scale.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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/VgKUB76upcCtBSyuehtPUFaP9dD5ae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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data_forecasts, facet = ~ horizon,\n",
    "     data_actual = test,\n",
    "     actual_indices = test$Time) + \n",
    "  scale_color_manual(values = c(\"Python LASSO\" = \"#ffd43b\", \"R Random Forest\" = \"#276DC2\")) +\n",
    "  theme(axis.text.x = element_text(angle = 45, hjust = 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::combine_forecasts()`\n",
    "\n",
    "* For each of `Python` and `R`, our 3 direct-horizon forecast models have been separately trained and are producing distinct forecasts at various horizons. The first ensemble is to combine the 3 direct-horizon forecasts into a single forecast. The second ensemble--which is optional--is to average different ML models in a cross-sectional way at each forecast step into the future.\n",
    "  \n",
    "  \n",
    "* Below we'll create an ensemble of the `Python` LASSO and the `R` Random Forest models using the strategy outlined at the end of the [forecast combination vignette](https://nredell.github.io/forecastML/doc/combine_forecasts)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_combined_py <- forecastML::combine_forecasts(data_forecasts_py)\n",
    "\n",
    "data_combined_r <- forecastML::combine_forecasts(data_forecasts_r)\n",
    "\n",
    "data_combined <- forecastML::combine_forecasts(data_forecasts, aggregate = stats::median)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Custom plot - Individual forecasts on 1 plot\n",
    "\n",
    "* `forecastML` was written with flexibility in mind. In this context, that means that the built-in plots can often be extended in a straightfoward way using the various function returns in the `forecastML` pipeline. The **black** line below shows the ensemble forecast."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hB0XYKegKAlco7ikJ7LMN8IIGiGWONIG05+QffygJDzCbqqPugV9EGL5GhBBzxL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\ngg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data_combined, data_actual = test, actual_indices = test$Time) + \n",
    "  geom_line(data = data_combined_py, \n",
    "            aes(x = forecast_period, y = Demand_pred), color = \"#ffd43b\") + \n",
    "  geom_point(data = data_combined_py, \n",
    "             aes(x = forecast_period, y = Demand_pred), color = \"#ffd43b\") + \n",
    "  geom_line(data = data_combined_r, \n",
    "            aes(x = forecast_period, y = Demand_pred), color = \"#276DC2\") + \n",
    "  geom_point(data = data_combined_r, \n",
    "             aes(x = forecast_period, y = Demand_pred), color = \"#276DC2\") + \n",
    "  facet_wrap(~ NULL) + theme(legend.position = \"none\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "## Forecast error on the test dataset with `forecastML::return_error()`\n",
    "\n",
    "* Remember that, although we're assessing forecast error below on the test dataset, we still haven't trained on the data in our 1 historical validation window. So this isn't 100% the linear workflow if you were trying to, say, win a Kaggle competition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_error_py <- forecastML::return_error(data_combined_py, data_test = test, test_indices = test$Time)\n",
    "\n",
    "data_error_r <- forecastML::return_error(data_combined_r, data_test = test, test_indices = test$Time)\n",
    "\n",
    "data_error <- forecastML::return_error(data_combined, data_test = test, test_indices = test$Time)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Custom plot - MAE forecast error by forecast horizon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QKBSyMEzqdVBH11gK0gaAOCToHApUHQ\npakjMIIWQNCqeEpgBJ2NOgIjaAEErYqnBEbQ2agjMIIWQNCqeEpgBJ2NOgIjaAEErYqnBEbQ\n2agjMIIWQNCqeErgjFrNbOinVFgvCNqAoFMgcGnCgXNKFUHfDARtQNApELg0CLo0dQRG0AII\nWhUPCYyg81FHYAQtgKBV8ZDACDofdQRG0AIIWhUPCYyg81FHYAQtgKBV8ZDACDofdQRG0AII\nWhUPCYyg81FHYAQtgKBV8YzAeZ2ad2/PqLBmELQBQadA4NIg6NLUERhBCyBoVTwjMILOSB2B\nEbQAglbFMwIj6IzUERhBCyBoVTwi8AtBZ6SOwAhaAEGr4hGBM593gaDvBYI2IOgUCFyaQODM\nE2gEfTMQtAFBp0Dg0oQFnfcYWXf4hArrBkEbEHQKBC4Ngi5NHYERtACCVsUDAufucCDom4Gg\nDQg6BQKXJijozMdA0LcCQRsQdAoELs0icP4JNIK+FwjagKBTIHBpQoLOfQwEfSsQtAFBp0Dg\n0viBC0ygEfS9QNAGBJ0CgUsTEHT+g+Tc6e0rrB4EbUDQKRC4NAi6NHUERtACCFoVdw9cosOB\noO8FgjYg6BQIXJqloAscBEHfCQRtQNApELg0buAyE2gEfSsQtAFBp0Dg0iwEXeIgCPpOIGjD\nuqDfPon97EHQqrh34EITaAR9KxC0YVXQb8P/pJ8DCFoV9w5cyM9Zd3zvCt8BBG1A0CkQuDQI\nujR1BK5P0B0I+mbcOnCpDgeCvhUI2pBB0P/X8RcgD58avd2eQQd1CvqtZQZ9L+4cuNwEOueu\n71zhe8AM2oCgUyBwaVxBFzsMgr4PCNqQIug3+38I+g7cJ/AgzDlwwQl0zp3fp8IDdQSuUdBv\n8/8R9E24TeBRmH8XS8oe7zC3qfBIHYErFPSb9QNB34TbBB6ntCcKOs/ub1PhkToC1yfot7fh\nI4N8kvBG3CXwayHooh2ONp//71LhiToC1yfoRBC0Ku4S+DUa2hZ08SPm2M9dKjxRR2AELYCg\nVXGXwAtBl55AZ/sLcJcKT9QRGEELIGhV3CXwazS0JegTDplhN3ep8EQdgRG0AIJWxU0Cd7I8\nWdCZDnGTCs/UERhBCyBoVdwkcOfKztJ/pwVnCDrDMW5S4Zk6AiNoAQStipsE7lVpjPl3vF/c\nz5mm0Dep8EwdgRG0AIJWxU0CD6ocBP06x895/gzcpMIzdQRG0AIIWhX3CPyaBf2aT+g45biH\n93GPClvUERhBCyBoVdwj8CTK18hpxz18pHtU2KKOwAhaAEGr4h6BfUGff+D93KPCFnUERtAC\nCFoV9wg8e/JUPWc53D0qbFFHYAQtgKBVcYvAtiZP9XOOKfQtKmxTR2AELYCgVXGLwLYlTw6M\noPWDoA0IOgUCl+BaQR809C0qbFNHYAQtgKBVcYfArwsFfXwKfYcKO9QRGEELIGhV3CGw48gL\nBH3M0HeosEMdgRG0AIJWxR0CXyrow1PoO1TYoY7ACFoAQaviDoER9KnUERhBCyBoVdwg8Oty\nQR8y9A0q7FJHYAQtgKBVcYPAriDPD4yglYOgDQg6BQLnR4Ggjxj6BhV2qSMwghZA0Kq4QeCr\nBX1wCn2DCrvUERhBCyBoVegP/NIg6AOG1l9hjzoCI2gBBK0K/YE9O14RGEGrBkEbEHQKBM4O\ngj6ZOgIjaAEErQr9gXUIer+h9VfYo47ACFoAQatCfWBfjpcERtCaQdAGBJ0CgXPjuxFBl6aO\nwAhaAEGrQn1gLYLebWj1FfapIzCCFkDQqlAfWIWgj0yh1VfYp47ACFoAQatCfWAEfTZ1BEbQ\nAghaFdoDL8yIoEtTR2AELYCgVaE9sB5B7zW09govqCMwghZA0KrQHviQoJuJ/DmS0V7hBXUE\nRtACCFoV2gMfEXTT5DM0gtYLgjYg6BQInJlcgj46fBG0XhC0AUGnQODMHBT0fOugovc3obVX\neEEdgRG0AIJWhfLASy2mB7adnMXQ+zZUXuEldQRG0AIIWhXKA+cS9PF2B4JWC4I2IOgUCJyX\nbII+/JYhglYLgjYg6BQInJeMgj5o6N1NaOUVXlJHYAQtgKBVoTxwTkGvP7AxShrKK7ykjsAI\nWgBBq0J34IAUkwPLGkbQUeoIjKAFELQqdAcuJuh9PY7tG7XaKxygjsAIWgBBq0J34DKC3jeF\n3tuE1l3hAHUERtACCFoVugOXE/R5U2jdFQ5QR2AELYCgVaE78AFBRx2MoCPUERhBCyBoVagO\nHFIigi5NHYERtACCVoXqwCUFvX0872xCq65wiDoCI2gBBK0K1YGLCfrMKbTqCoeoIzCCFkDQ\nqlAduKigd02hN2+jvMIh6giMoAUQtCpUBz4g6DUBI2iROgIjaAEErQrVgcsKevOI3teEVl3h\nEHUERtACCFoVmgMHfZhJ0IFLKe0MtIbmCgepIzCCFkDQqtAc+ERBp13iDkGrBEEbEHQKBM5I\naUG734iFoAfqCIygBRC0KjQHPiDoBN1OVk6/SPSuJrTmCgepIzCCFkDQqtAcuKygvW/BSnrT\nEEFrBEEbEHQKBM5H2Ib5BO3NnUv1OBRXOEwdgRG0AIJWheLA5QXd2qfblepxKK5wmDoCI2gB\nBK0KxYEPCHrPx1BK9TgUVzhMHYERtACCVoXiwAj6GuoIjKAFELQqFAdWKuithlZc4TB1BEbQ\nAghaFYoDaxT0jim04gqHqSMwghZA0KrQG1hQ4fWC3mhovRUWqCMwghZA0KrQG/iAoHdd7bnU\nFFpvhQXqCIygBRC0KvQGRtAXUUdgBC2AoFWhN7BeQW8ztN4KC9QRGEELIGhV6A28X9D7/Jy6\nGYLWBoI2IOgUCJyN3YLe9XVW7RZBbzK03goL1BEYQQsgaFXoDbxX0Hv9nDzxRtDKQNAGBJ0C\ngbOxU9C7/bxF0FsMrbfCAnUERtACCFoVegPvE/R+P5eaQuutsEAdgRG0AIJWhd7AuwR9xM8I\nuqeOwAhaAEGrQm/gPYI+5OdCPQ69FRaoIzCCFkDQqtAbeKegDxwxeWsErQoEbUDQKRA4F5IE\nEXRp6giMoAUQtCrUBt4j6GMdDgTdU0dgBC2AoFWhNvBOQR85JILuqCMwghZA0BnZ/hWmPmor\nfIGgy5zGobbCEnUERtACCPoIrhj2fMm0h9oKaxb0psKrrbBEHYERtACCTiN4Lpe77LXnS6Y9\n1FZ4h6APtqARdE8dgRG0AIJO4jWyWCje3YXaCu8T9LFjImhDHYERtACCTuH1Chjau78U+A7U\nVhhBX0UdgRG0AIJOoTdA0Mgv4e4+1FYYQV9FHYERtACCTmAWr6Xg7qZ4dydqK7xd0Idb0GVO\n41BbYYk6AiNoAQSdgDdPtm44gs5wHofaCu8S9NGDIui2lsAIWgBBr7NobAw/25CvjxlabYUR\n9FXUERhBCyDodZZn0/menn4i6AkEnYc6AiNoAQS9SujsutadOSPoBRla0EXeJVRbYYk6AiNo\nAQS9yuLV75yv4bY6jvY41FZ4j6APHxRBt7UERtACCHqV5avfPp/Oe7MQQQ8g6EzUERhBCyDo\nNUKTYu9dw/B5eHtQW+FLBF2iCa22whJ1BEbQAgh6jdCL3/tAoXce3oGDqa3wVkHnaEEjaEMd\ngRG0AIJeYXVKvPxA4YGjaa2w+Kwigs5wWARdS2AELYCgV1h/7S8/AL7/aForjKAvo47ACFoA\nQcdJ8K13CQ4EbUDQuagjMIIWQNBxUl76iw+y7D+c1gpvFXSeFnSJ0zi0VlikjsAIWuD//kIE\nMzlOWGv7Jjdj63P6NGuOwybv5ok1r4rjgm4GUlf3fuaGGXQKhwPvmQ4fmUJrrfCOGXSW4+bv\ncWitsEgdgTMIet/qCPpKEHQmEPRl1BEYQQsg6Bi7Tsk4ch6H1gpvFHSmFjSCbmsJHPdQE8Zd\nx7o1PNa4P4flzp1us2zDNRjnGAg6xj7VIuhsAx5BVxI4q6AH8Tat97OxH5xXatzN84CgU0DQ\nmUDQl1FH4AyCnhY6Ym6XovbtjaAv42Dgnc2KAz0OrRW+UNBJe0LQeri8Bz0Jdxg7vrgXgt5y\n9sf2OMdA0BH2irZ2QWcc7wi6jsBFBD03MrzlgRl0bhB0Cgg6E5sFnevA2XscWissUkfgQoIO\ntjoQtBqOBd7dqkDQCDobdQQuIWjp5+lvElpjePMrA0HL7Pbs/ia01gpvEnTOjl72JrTWCovU\nETjnJwmtHrR3ml1r2/q80+zm00cQtMtFgt6/pdYKbxV0viMj6KsDbIVrcRgQdAqHAh84GaNq\nQeedjyDoqwNsBUEbEHQKRwV9+qZaK7xB0Jn/vYigrw6wFQRtQNApXCjofdtqrfA2Qec8cqLv\nEbQaELQBQadwlaB3b6u0wvLTWQTO/oYLgr4ZCNqAoFM4EvjQd1dVLei8x0bQNwNBGxB0CgcF\nfWjjXVsrrXC6oPOfsZS5Ca20wjJ1BH64oKULiKyDoCWOfT13pYIucVGDvFNopRWWqSMwghZA\n0ALHvp27YkFnPziCvhcI2sBHvVM4JugjR65T0CU+koWgbwaCNiDoFC4V9J7tlVZ4g6DzHxxB\n3wsEbQiP2V/f3zbuB0GHOdjh2Ct4pRVOFHSRCXTiXhG0FhC0ITBkf357axoEbXNI0McOXamg\nSxwdQd8KBG3wh+zPb2ai8e3n1v0g6DDe63373LBCQZeZQCPom4GgDc6Q7e3cNP+27wdBh3Ff\n7ztOkdnXI1Fa4WRBFzl61ia00grL1BH40YIe5s67Xh4IOozzcpfOYozerU7QpSbQeZvQSiss\nU0fghwv66792x6cIDQg6jPVyHy8DvjR09G5tgi7m57w9DqUVlqkj8MMFzQw6zO7ASz97N9fv\n7upxKK1woqBLHR5B3wkEbaAHnUIGQbvate94U+rFBLsuQRecQCPoW3GRoINvE8XGTbO86c7F\nFgs3xfHuD2dx/Nq6HwQdZHq1B7oa9q/Qm13XLehih096iSBoJVwlaOfHcCtN0M1wuwn9b99F\n6DgPOonDgg78TW7cL6IcHvd0be9jC0orvC7okhPoNPsjaCXcVtDzHqx9LXa7LY4HnyR0OSro\nkHbmtwzHu+1C1+M+NhtaaYWTBF3w+Cn6R9BKKCDojzDOOpNJ5xlTM3139/zF3lbrwtq08Rcs\nbm0d3lyLI4UMgl4+5p5x50ydD0+hdVY48kSGwGUn0P77r0EQtBKUCLqf/w6T4FHA431rg3mi\nHOpAZxH0W2OxcT8IOkhM0N7bgb6uFzvZgs4Kh57I8Ez/toG3RwuQzdA6KxyhjsAZBD0NQ0vK\nk5i9n9YPtxfivDfor7QFe/2vCFpgb+BIh2O53C57NYIeR9vfneNuM+vHQNA6uLYH3W4WdBPY\nfLqVRdA/mvf/Np++MYCgQ0Qn0K3/pq43nfb3sgWdFV4+kcanfIjVoyBoHVwu6LG90SYK2hvB\n+QX9x5y+0Xz7347ToBF0kP61nioebzpt72WroXVWOCjo9kw7D8eMHglB6+B2gm7tB71buc7i\n+PXf++fw/fLf7637QdAhJkFv3vJgj0NnhcOCbou/N7g8aOxoCFoHNxP07OlmenS+lfE86D8/\nvjScB+1ySNC77HOwx6GzwovnMT/LUwPHfyMIWgfXC3pUq3X6nPX+4WRm999/1lrOrUyfJOz4\n95U3CR2OCnrHprUIerh1buDoawVB60DBtThO/GddegRm0EuuEfS02fYmtM4KqxF01NAIWgcI\nOhBh6EH/+LN1Pwg6wP4OR3twCq2zwv7TaC4TdPSvZlK1dVY4Qh2Bcwr6zPdFRBZncbx9+8lZ\nHD4HBb1r4zoEPd68QNDHptA6KxyhjsCPvtwo50FLHBD07hMUvB7Hto11VliRoGN/NxG0ChC0\nwR6lfJJQ4pigdx708YJuLha09ItB0CpA0AZ7kHItDomrBD1uuvldQp0VXgp6un1+YHmQI2gV\nIGhDrj44gg7w+Uo/8hGMA1NonRVWJWj5TyeCVgGCNiDoFPYFPjaBfrygm+sFHf7dIGgVIGgD\ngk7hMkFbPY5Nm+qs8ELQ850rAh8ytM4KR6gjMIIWQNBLjgq63d+E1llhZYIWfzkIWgMI2oCg\nU9gt6GMXAdrf49BZYedJNCoEHfz1IGgNIGgDgk7hOkHv7HGorHBkAn1RYAStGARtQNApXCTo\nFkGXBUErBkEbEHQKKgS9xdAqKxzpcFwn6NDvB0FrAEEbEHQKuwIf9/P+HofKCvuCth+7KPD+\nKbTKCseoIzCCFjHILpIAACAASURBVEDQCzIIenePQ2WFEfSV1BEYQQsg6AUI2sN+Cn5z4TpB\n7+xxqKxwjDoCI2gBBL0gk6CbaW8btlNZYU/QzmNXBUbQarlI0N7FiNauTRR7ge+7rFH6/reA\noBfkEHRrC3qDoVVWGEFfSR2B830nYRO8K66+9bHUtRB0CvsFPd75+Nh35J09DpUVVirowEsA\nQSsAQafvYx0EvcAW9MfHTkPv7HGorLD1DBZevCwwgtZKAUG/wjjrRAQ9jNpmHDTN8H3f7nKr\nPTLvdF5jHvxNY98TQNAp7Alsdzg+evYc+rGCdh/TJeiEYquscIw6ApcUdDP+bOb7zWJ5s9x2\nsaW7u2hkBJ3CQUF/TGzfzb4mtMoKaxX0rim0ygrHqCNwBkHH3yT0zRr4OQu6mWbOgTXWmicp\nj6aDoH2sDkdn5p2G3tfjUFnh+QksrXhdYAStlCt70E347tCUGBatC9rfydTZmCfbCDoHxwQ9\ninnfLPqhgvYeQ9ClqSNwrjcJm9Bdq7VxRNDWsZoWQefgkKAtKe/pdCDosgR7HAj6etQJek3M\n2wVNDzoTRwTtCHlHM3oSCIIuA4LWybWn2TXLu2NbwtZtqOWRImh/s7U4h0HQPpagneV7DD3u\nMNnQKis85Q9MWhF0aeoIXPQ86OG0usa733pvBS4F7azhnWa38qVLCDqFHYGDE+iBbYbe0+NQ\nWWFb0P5j1wp6h6FVVjhGHYG5FocAgvYYBC2o2F0c9/WeHofKCisV9L4ptMoKx6gjMIIWQNAe\ns6CDD9tOXutLP0TQsQ4Hgi5OHYERtACC9ugFLXt3euQjgLvqjia0xgrHJtBXC3oRCEFfDoI2\nIOgUtgd+TYKW1hhEPAg5ZugdTWiNFVYr6FAgBH05CNqAoFPYHPi10uEwdCK2dCwaekcTWmOF\nx/TBN+WuFrSfCEFfDoI2IOgU9gi6iXY4DGLrWZpCP0bQywevDYygFYKgDQg6ha2BX7OgY6tJ\nbw0GptDjbhMDaKzwrQS9WmuNFY5SR2AELYCgLbp38z5f9KunO0fO8bDvbn+XUGOFdQt66xRa\nY4Wj1BEYQQsgaIvBz2sTaJnDTWiNFR7Ch6/veXFgBK0PBG1A0ClsC5w8gRY53OPQWOFZ0IEH\nrxe0lwpBXw2CNiDoFDYF7hsRvaD3HhBBnwyCVgeCNiDoFLYKuj3W4VhMoTc3oTVWuM8ufAXb\n1YERtDoQtAFBp7Al8NjgONDhaP0p9OYmtMYKT4IOPXh14M09jqsDb6aOwAhaAEEPvHJMoGNT\n6KTNNVZYtaA3T6EvD7yVOgIjaAEEPWD7+YCgl1Poee8JaKwwgr6UOgIjaAEEPTA2OI5NoCOC\nTjK0xgqrF7QbDEFfDII2IOgU0gMPnyFcuQxHAu4EfGsTWmOFdQt6EQxBXwyCNiDoFDYJuh39\nfEjQx3ocGiusX9BOMgR9MQjagKBT2CToJvhVhJtZTKHH/adsrLHCygXtJ0PQF4OgDQg6he2C\nPuxnbxf3F3TUzxoCb+txKAi8jToCI2gBBN1hXQc6h6DnfYz/AE98l1Bhhe8g6A1TaAWBt1FH\nYAQtgKA7Mvr50BRaYYXVC3pbj0ND4E3UERhBCyDojrVvItyEP4Uej5BgaIUVRtDXUkdgBC2A\noDtWv4lwEyFBd4ZeVbTCCiPoa6kjMIIWQNCGrgWdzc++oG1D3+8LmfQL2guHoK8FQRsQdAob\nBH3wIkkOwR5HkqEVVvh2go4bWkXgLdQRGEELIGiDEXQ+Pws9jjahzaGwwgj6WuoIjKAFELTh\n8yWd08/OFHrx7++b/QMcQV9LHYERtACCbntr5vSzM4Vubt4hRdDXUkdgBC2AoNupw5HxwNEp\ndGQ7hRVG0NdSR+AqBf3W//+T0M8eBN3m73C0/hTaO5i8mb4Kz19kEERH4A1/A3UE3kAdgWsU\n9ODj4X/+zwEE3Y6CznpkS/i3F3R7M0FHS6wj8AbqCFyhoN9aBH2doFtH0Dee3yHoi6kjcIWC\nbhF0YuD87xG2kR7HvQT9QtAXU0dgBL0U9P91/IXez5l3+jHv8lMf7tEyH6okQ1r3KajDi3ev\nEsMnCJoZtEiJCbTc47jdDNr8UD6D3vCPFCWB06kjMIJG0CLFBB1+m/BO+ngh6KupIzCCRtAS\nfQs6/8EfIuju570EHSuxksDp1BEYQSNoiTITaAR9JghaDwjagKBTuFrQw17Tm9DKKvxC0JdT\nR+B6Bc0nCdco1OEQp9D3EnR/A0FfRh2BqxR0Cgi6VAt6V49DWYVXJ9BqAt+1wuvUERhBCyDo\nUh0Or8fhHlHaRFmFEfT11BEYQQsg6GITaGsKndyE1lXh9Ra0msDJPQ4tgZOpIzCCFqhe0OU6\nHHua0LoqvN6CVhMYQasBQRsQdArrgYtch2MEQZ8GglYDgjYg6BSSBF3Mz9KJdncR9OtGgk5u\nQqsJnEodgRG0QOWCLjqB3jGFVlXhOSaCvo46AiNogboF/SrwXSo2CPo0ELQWELQBQaewEviV\n/8sIXW4t6NeNBS2XWE3gVOoIjKAFahd0U1rQ25rQmipspUTQ11FHYAQtULOgxwl0OUELU2gE\nXYDEHoeewIlkCBz7Hvn8IGgDgk4hGvhVfAK9vcehqMJJHQ5FgRG0RPQrIvKDoA0IOoU1Qbcn\nCHpTj0NRhZMm0IoCI2iB1+tcQyNoA4JOYU3QTeEOh/TFV3fQB4LWwdHALwR9BQg6hSRBF03g\nfrn3+Fu7gT5e9xa0WGI9gRPJI+gTDY2gDQg6BVWCtgx9D0FPtzMK+mNgbywZBB2kkzOCPh0E\nncKqoEt3ONqPbYbWU+H8gv5YcCjggrQeh54KJ3IscD95PnUKjaANCDqFFEEXjuAcYTK0en28\nMgt6aefshkbQAYYyIOizQdApxAKfMoH2BD0ZWr0+nICHBb1UcgFDI+glr1nQpxkaQRsQdAoJ\ngi4d4WNh6OHgwbXVVDinoKX5cmZFI+gFs5cR9Mkg6BQUCNqbQg8a0a6PV0ZBy3PlvIZukgyt\npcLJHBT0fOssQyNoA4JOYUXQJ3Q4biHoZRg33xFBR1sZ2Q1t3UPQjpUR9Lkg6BTWBV0+w7LH\nETH0JRUOzK6yCXpNwTkNjaBdnN/reVNoBG1A0CloEPSmKfQVFQ58kCG5w7EWeH2KnNHQi6/m\nDZX4UWM4jlsABH0qCDoFBJ3Aa/lZs+QJdDxwUgcjr6Gte2FDP2oMx1n8Ts9xNII2IOgUVgV9\nRojgeRy6BO1fUCePoBM7zKUEHTb0o8ZwHO/pvwJ/iUuAoA0IOgUVgg6eCq1H0PNnzV7uoomd\ngk59BzDfFNoPGrLRo8ZwnFDj6gRDI2gDgk5Bo6BbfYIefwonze4TdLp3cwp61dCPGsNRgkPs\nBEMjaAOCTmFN0Oek2NDjuFDQlqFzCHrDvLjcFDpg6EeN4SiSiBH0GSDoFCKBz5tAB3ocrR5B\nWwobDe1bbY+gN0m3nKCXhn7SGI6DoK8EQaegVdBij+MSQTt3Ahe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KIKNB0FenWWFsQp8v6ON/vPQOCbkNrULQ4scH/dx6K+zxGr4GAUEb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\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_plot <- dplyr::bind_rows(data_error_py$error_by_horizon, \n",
    "                              data_error_r$error_by_horizon, \n",
    "                              data_error$error_by_horizon)\n",
    "\n",
    "p <- ggplot(data_plot, aes(horizon / records_per_day, mae, color = model))\n",
    "p <- p + geom_line(size = 1.05)\n",
    "p <- p + scale_color_manual(values = c(\"Python LASSO\" = \"#ffd43b\", \"R Random Forest\" = \"#276DC2\", \n",
    "                                       \"Ensemble\" = \"black\"))\n",
    "p <- p + theme_bw()\n",
    "p <- p + xlab(\"Forecast horizon (rescaled to daily level)\") + ylab(\"MAE\") + labs(color = NULL) + \n",
    "  ggtitle(\"Forecast Error on Test Data - By forecast horizon\")\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Custom plot - MAE forecast error collapsed across horizons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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L2WGnszweClxlbDRqnmyg2AXn1kvfdAmy4vnm9gdlPpx+u7v/Ppqzh+Lj7o7yTs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\nTjPQzjnXaQbaOec67f8BHXR37sXUB7EAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_plot <- dplyr::bind_rows(data_error_py$error_global,\n",
    "                              data_error_r$error_global,\n",
    "                              data_error$error_global)\n",
    "\n",
    "p <- ggplot(data_plot, aes(model, mae, fill = model))\n",
    "p <- p + geom_col()\n",
    "p <- p + scale_fill_manual(values = c(\"Python LASSO\" = \"#ffd43b\", \"R Random Forest\" = \"#276DC2\",\n",
    "                                      \"Ensemble\" = \"black\"))\n",
    "p <- p + theme_bw()\n",
    "p <- p + xlab(\"Model\") + ylab(\"MAE\") + labs(fill = NULL) + \n",
    "  ggtitle(\"Forecast Error on Test Data - Collapsed across forecast horizons\")\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n",
    "\n",
    "## Retrain with All Data & Produce Final Forecasts\n",
    "\n",
    "* Set `create_windows(..., window_length = 0)` to train over all data. Historical predictions will essentially produce fit statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_all <- dplyr::bind_rows(train, test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::create_lagged_df(type = \"train\")`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_all$Time <- NULL  # Still in the test dataset at this point.\n",
    "data_all$Date <- NULL  # Still in the test dataset at this point.\n",
    "\n",
    "dates <- as.POSIXct(data[, \"Time\", drop = TRUE])  # All dates from train + test.\n",
    "\n",
    "data_train <- forecastML::create_lagged_df(data_all, type = \"train\", outcome_col = 1,\n",
    "                                           lookback = lookback, horizons = horizons,\n",
    "                                           dates = dates, frequency = frequency,\n",
    "                                           dynamic_features = dynamic_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::create_windows(window_length = 0)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oZWQdAqAkGfkVUEPSwnBA3ZIGgV0Zl4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\nQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "windows <- forecastML::create_windows(data_train, window_length = 0)\n",
    "\n",
    "plot(windows, data_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::train_model()`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `Python` model functions\n",
    "#### Fix hyperparameters\n",
    "\n",
    "* The hyperparameters will be created in `R` and passed into the final `Python` modeling function; however, they could have been created in `Python`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$`48`</dt>\n",
       "\t\t<dd><strong>$alpha</strong> = 0.690366782170224</dd>\n",
       "\t<dt>$`96`</dt>\n",
       "\t\t<dd><strong>$alpha</strong> = 0.905489147902536</dd>\n",
       "\t<dt>$`144`</dt>\n",
       "\t\t<dd><strong>$alpha</strong> = 3.91964636388139</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$`48`] \\textbf{\\$alpha} = 0.690366782170224\n",
       "\\item[\\$`96`] \\textbf{\\$alpha} = 0.905489147902536\n",
       "\\item[\\$`144`] \\textbf{\\$alpha} = 3.91964636388139\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$`48`\n",
       ":   **$alpha** = 0.690366782170224\n",
       "$`96`\n",
       ":   **$alpha** = 0.905489147902536\n",
       "$`144`\n",
       ":   **$alpha** = 3.91964636388139\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$`48`\n",
       "$`48`$alpha\n",
       "[1] 0.6903668\n",
       "\n",
       "\n",
       "$`96`\n",
       "$`96`$alpha\n",
       "[1] 0.9054891\n",
       "\n",
       "\n",
       "$`144`\n",
       "$`144`$alpha\n",
       "[1] 3.919646\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "py_lasso_alphas <- lapply(model_results_py, function(x) {\n",
    "  x$window_1$model$model$alpha_  # $alpha_ is an attribute in sklearn.linear_model.LassoCV().fit()\n",
    "})\n",
    "\n",
    "# Heads up: reticulate seems to convert numeric R list names (i.e., `48` with backticks) \n",
    "# into character dict keys in Python. So we'll be explicit and use and expect characters in Python.\n",
    "hyperparameters = list(\"48\" = list('alpha' = py_lasso_alphas[[1]]),\n",
    "                       \"96\" = list('alpha' = py_lasso_alphas[[2]]),\n",
    "                       \"144\" = list('alpha' = py_lasso_alphas[[3]]))\n",
    "\n",
    "hyperparameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `Python` model function in `model_script.py`\n",
    "\n",
    "* This is the final modeling function with fixed hyperparameters and no cross-validation.\n",
    "  \n",
    "  \n",
    "* **Arguments passed through the `R` wrapper:**\n",
    "    + **data:** The horizon-specific training dataset from create_lagged_df(type = \"train\").\n",
    "    + **hyperparameters:** The optimal `sklearn` LASSO hyperparameters passed from `R`.\n",
    "    + There are no argument name restrictions in any user-defined function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<span style=white-space:pre-wrap>'\\ndef py_model_fun_final(data, hyperparameters):\\n  \\n  horizon = int(data.horizons)  # Horizons: 48, 96, and 144.\\n  \\n  X = data.iloc[:, 1:]\\n  y = data.iloc[:, 0]\\n  \\n  scaler = StandardScaler()\\n  X = scaler.fit_transform(X)\\n  \\n  alpha = hyperparameters[str(horizon)][\\'alpha\\']\\n  \\n  model_lasso = linear_model.Lasso(alpha = alpha)  # No cross-validation at this point.\\n  \\n  model_lasso.fit(X = X, y = y)\\n  \\n  return({\\'model\\': model_lasso, \\'scaler\\': scaler, \\'horizon\\': horizon})\\n'</span>"
      ],
      "text/latex": [
       "'\\textbackslash{}ndef py\\_model\\_fun\\_final(data, hyperparameters):\\textbackslash{}n  \\textbackslash{}n  horizon = int(data.horizons)  \\# Horizons: 48, 96, and 144.\\textbackslash{}n  \\textbackslash{}n  X = data.iloc{[}:, 1:{]}\\textbackslash{}n  y = data.iloc{[}:, 0{]}\\textbackslash{}n  \\textbackslash{}n  scaler = StandardScaler()\\textbackslash{}n  X = scaler.fit\\_transform(X)\\textbackslash{}n  \\textbackslash{}n  alpha = hyperparameters{[}str(horizon){]}{[}\\textbackslash{}'alpha\\textbackslash{}'{]}\\textbackslash{}n  \\textbackslash{}n  model\\_lasso = linear\\_model.Lasso(alpha = alpha)  \\# No cross-validation at this point.\\textbackslash{}n  \\textbackslash{}n  model\\_lasso.fit(X = X, y = y)\\textbackslash{}n  \\textbackslash{}n  return(\\{\\textbackslash{}'model\\textbackslash{}': model\\_lasso, \\textbackslash{}'scaler\\textbackslash{}': scaler, \\textbackslash{}'horizon\\textbackslash{}': horizon\\})\\textbackslash{}n'"
      ],
      "text/markdown": [
       "<span style=white-space:pre-wrap>'\\ndef py_model_fun_final(data, hyperparameters):\\n  \\n  horizon = int(data.horizons)  # Horizons: 48, 96, and 144.\\n  \\n  X = data.iloc[:, 1:]\\n  y = data.iloc[:, 0]\\n  \\n  scaler = StandardScaler()\\n  X = scaler.fit_transform(X)\\n  \\n  alpha = hyperparameters[str(horizon)][\\'alpha\\']\\n  \\n  model_lasso = linear_model.Lasso(alpha = alpha)  # No cross-validation at this point.\\n  \\n  model_lasso.fit(X = X, y = y)\\n  \\n  return({\\'model\\': model_lasso, \\'scaler\\': scaler, \\'horizon\\': horizon})\\n'</span>"
      ],
      "text/plain": [
       "[1] \"\\ndef py_model_fun_final(data, hyperparameters):\\n  \\n  horizon = int(data.horizons)  # Horizons: 48, 96, and 144.\\n  \\n  X = data.iloc[:, 1:]\\n  y = data.iloc[:, 0]\\n  \\n  scaler = StandardScaler()\\n  X = scaler.fit_transform(X)\\n  \\n  alpha = hyperparameters[str(horizon)]['alpha']\\n  \\n  model_lasso = linear_model.Lasso(alpha = alpha)  # No cross-validation at this point.\\n  \\n  model_lasso.fit(X = X, y = y)\\n  \\n  return({'model': model_lasso, 'scaler': scaler, 'horizon': horizon})\\n\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\n",
    "def py_model_fun_final(data, hyperparameters):\n",
    "  \n",
    "  horizon = int(data.horizons)  # Horizons: 48, 96, and 144.\n",
    "  \n",
    "  X = data.iloc[:, 1:]\n",
    "  y = data.iloc[:, 0]\n",
    "  \n",
    "  scaler = StandardScaler()\n",
    "  X = scaler.fit_transform(X)\n",
    "  \n",
    "  alpha = hyperparameters[str(horizon)]['alpha']\n",
    "  \n",
    "  model_lasso = linear_model.Lasso(alpha = alpha)  # No cross-validation at this point.\n",
    "  \n",
    "  model_lasso.fit(X = X, y = y)\n",
    "  \n",
    "  return({'model': model_lasso, 'scaler': scaler, 'horizon': horizon})\n",
    "\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `R` wrapper for `Python` model function in `model_script.py`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_wrapper_for_py_model_fun_final <- function(data, hyperparameters) {\n",
    "  \n",
    "  reticulate::source_python(\"model_script.py\")\n",
    "  \n",
    "  py_model_return <- reticulate::py$py_model_fun_final(data, hyperparameters)\n",
    "  \n",
    "  horizon <- py_model_return$horizon\n",
    "  \n",
    "  reticulate::py_save_object(py_model_return, paste0(\"py_model_final_horizon_\", horizon, \".pkl\"), \n",
    "                             pickle = \"pickle\")\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `Python` - Model training with no internal or external CV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "future::plan(future::multiprocess)\n",
    "\n",
    "model_results_py_final <- forecastML::train_model(data_train,\n",
    "                                                  windows = windows,\n",
    "                                                  model_name = \"Python LASSO\",\n",
    "                                                  model_function = r_wrapper_for_py_model_fun_final,\n",
    "                                                  hyperparameters = hyperparameters,  # Passed in ...\n",
    "                                                  use_future = TRUE,  # Parallel training.\n",
    "                                                  python = TRUE\n",
    "                                                  )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load models into the `forecast_results` object\n",
    "\n",
    "* This is the same step 3 in the `Python` workflow outlined earlier.\n",
    "  \n",
    "  \n",
    "* Read the pickeled trained model and any meta-data from disk and place it in the `trained_model_name$horizon_n$window_n$model` list slot.\n",
    "  \n",
    "  \n",
    "* `[[i]]` below indexes `$horizon_48`, `$horizon_96`, and `$horizon_144`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "$model\n",
       "Lasso(alpha=0.6903667821702241, copy_X=True, fit_intercept=True, max_iter=1000,\n",
       "      normalize=False, positive=False, precompute=False, random_state=None,\n",
       "      selection='cyclic', tol=0.0001, warm_start=False)\n",
       "\n",
       "$scaler\n",
       "StandardScaler(copy=True, with_mean=True, with_std=True)\n",
       "\n",
       "$horizon\n",
       "[1] 48\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for (i in seq_along(horizons)) {\n",
    "  \n",
    "  model_name <- paste0(\"py_model_final_horizon_\", horizons[i])\n",
    "  \n",
    "  model_results_py_final[[i]]$window_1$model <- reticulate::py_load_object(paste0(model_name, \".pkl\"), \n",
    "                                                                           pickle = \"pickle\")\n",
    "}\n",
    "\n",
    "model_results_py_final[[1]]$window_1$model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `R` - Model training with no internal or external CV\n",
    "\n",
    "* We didn't optimize hyperparameters in the Random Forest model so we'll re-use the model exploration training function without fixing hyperparameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "future::plan(future::multiprocess)\n",
    "\n",
    "model_results_r_final <- forecastML::train_model(data_train,\n",
    "                                                 windows = windows,\n",
    "                                                 model_name = \"R Random Forest\",\n",
    "                                                 model_function = r_model_fun,\n",
    "                                                 use_future = TRUE\n",
    "                                                 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::predict()` on historical data\n",
    "\n",
    "* Predicting on historical data with `create_windows(window_length = 0)` shows model fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_historical <- predict(model_results_py_final, model_results_r_final,\n",
    "                           prediction_function = list(r_wrapper_for_py_predict_fun, r_predict_fun),\n",
    "                           data = data_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `forecastML::plot()` historical fit for all data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uii3dfzSkDrklk5oPUGQGebcctP19UZsWkHdDorOxPQUW1U21EkRTTz71PKgI4f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\n5NNhNq4TDABaFgbUYTauEwwAegYb1wkGAC0LA+owG9cJBgA9g43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r/lpr18LkLcdaOkJAd3rz6RqA/mmfr7uRpzg8nQ+cQauOGbT7YoUw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\ncXT3SH8fSwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Without filtering the data, this will take a few seconds to plot.\n",
    "plot(data_historical)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `forecastML::plot()` historical fit for all 12AM demand for the 1-day-ahead horizon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4CuuAEpLgGgJVJrCQDNBUBX3IAUlwDQ\nEqm1BIDmAqArbkCKSwBoidRaAkBzAdAVNyDFJRoDoI9PrSUANBcAXXEDUlwCQEuk1hIAmguA\nrrgBKS4BoCVSawkAzQVAV9yAFJcA0BKptQSA5gKgK25AiksAaInUWgJAcwHQFTcgxSUAtERq\nLQGguQDoihuQ4hIAWiK1lgDQXAB0xQ1IcQkALZFaSwBoLgC64gakuASAlkitJQA0FwBdcQNS\nXAJAS6TWEgCaC4CuuAEpLgGgJVJrCQDNBUBX3IAUlwDQEqm1BIDmAqArbkCKSxgALZBaSwBo\nLgC64gakt4QB0BKptQSA5gKgK25AeksAaJHUWgJAcwHQFTcgvSUAtEhqLQGguQDoihuQ3hIA\nWiS1lgDQXAB0xQ1IbwkALZJaSwBoLgC64gaktwSAFkmtJQA0FwBdcQPSWwJAi6TWEgCaC4Cu\nuAHpLQGgRVJrCQDNBUBX3ID0lgDQIqm1BIDmAqArbkB6SwBokdRaAkBzAdAVNyC9JQC0SGot\nAaC5AOiKG5DeEgBaJLWWANBcAHTFDUhvCQAtklpLAGguALriBqS3BIAWSa0lrgj0vU32laKv\nfQB0xQ1IbwkALZJaS1wS6PTrffjnHt8HoKtuQHpLAGiR1FoCQAPoEzYgvSUAtEhqLXFBoO+l\nrwD6VA1IbwkALZJaS1wR6PwUNFEO9H9tPhFk//RAS7dAKskVgR7+4b4OwRF0xQ1Ibwlz8CG0\n/HqQb0D1lrgg0F2i8xsA+nwNSG8JAC2SWksAaAB9wgaktwSAFkmtJS4INE5xnL8B6S0BoEVS\na4mLAp3/B6DP1YD0lgDQIqm1xAWBHr1zEO8kPF0D0lsCQIuk1hJXBHpZAHTFDUhviRZnAH14\nai0BoLkA6IobkN4SAFoktZYA0FwAdMUNSG8JAC2SWksAaC4AuuIGpLcEgBZJrSUANBcAXXED\n0lsCQIuk1hIAmguArrgB6S0BoEVSawkAzQVAV9yA9JYA0CKptQSA5gKgK25AeksAaJHUWgJA\ncwHQFTcgvSUAtEhqLQGguQDoihuQ3hIAWiS1lgDQXAB0xQ1IbwkALZJaSwBoLgC64gaktwSA\nFkmtJQA0FwBdcQPSWwJAi6TWEgCaC4CuuAHpLQGgRVJrCQDNBUBX3ID0lgDQIqm1BIDmAqAr\nbkB6SwBokdRaAkBzAdAVNyC9JQC0SGotAaC5PAN0s1eJ7RWu3YD0llgE9I4bkPx6kG9A9ZYA\n0FwAdMUNSG8JAC2SWksAaC4AuuIGpLcEgBZJrSUANBcAXXED0lsCQIuk1hIAmguArrgB6S0B\noEVSawkAzQVAV9yA9JYA0CKptQSA5gKgK25AektMAt1kX19T4eDIN6B6SwBoLgC64gaktwSA\nFkmtJQA0FwBdcQPSWwJAi6TWEgCaC4CuuAHpLQGgRVJrCQDNBUBX3ID0lgDQIqm1BIDmAqAr\nbkB6SwDo6bxo35FfDQSg2wBo+U1RvgHpLQGgpwOgkwBoLgC64gaktwSAng6ATgKguQDoihuQ\n3hIAejoAOgmA5gKgK25AeksAaJ/iUgLoJACaC4CuuAHpLQGgfYalbJrCwMNKHBkADaA1bIry\nDUhvCQDtUwY6+s4eUOLIAGgArWFTlG9AeksAaJ9m+JcD2tr9hJZfDQSg2wBo+U1RvgHpLQGg\nfQD0fAA0FwBdcQPSWwJA+zigk8UF0EkANBcAXXED0lsCQPsA6PkAaC4AuuIGpLcEgPZp3D8A\nmg2A5qIa6KkZyG+K8g1IbwkA7QOg5wOguQDozZFvQHpLAGifAWgDoPkAaC4AenPkG5DeEgDa\npwf6sTImgN5rTcivBgLQbQC0/KYo34D0lgDQPh7oeG0A6CQAmguA3py8gchrpvKrgQD0dAMA\nPR8AzQVAbw6AdgHQUw06izugm2xgHwANoPn897k9zROP1TGDXVNX2xfnwVH3XzFN9vXUabrF\n7IHOh3Z5AH2NNTERAM0FR9CbgyNoFxxBTzTo3+PdAW3yoV1wBI0jaD4AenMAtAuAnmjQU2wA\n9FQANBcAvTkA2gVATzQA0AsCoLkA6M0B0C4AeqIBgF4QAM0FQG8OgHYB0BMNYqCbbGgXAA2g\n+QDozUkaNNlfzBApIRUAPdGgMQB6NgCaC4DeHADtAqAnGvRrgQfaAmgAzQdAbw6AdgHQEw08\n0Mn6yIHeaVXIrwYC0G0AtPymmALdAOg4ANqlXQsWQE8HQHMB0JsDoF0A9ESDx1p4EAygJwOg\nuQDozcmBFrmMQ341EICebMAB7W4DaALQfAD05gBol5VANwC6e+t3fwtAE4DmA6A3J3+REEBH\nAdAuZaANgI4DoLkA6M0B0C4AeqJBB3S3KqL1YVKgGwOgzxUALb8pZkCbvXay7SWkAqDZBv2n\n2M0BzZ6t36fEwQHQAFrDphg3aKLfWcVKiAVAsw0A9KIAaC4AenMAtMu4RA5SEgANoLMAaC4A\nenMSoA2AjnN1oP2SLQba0B7rQ341EIBucwmgJ1/alt8UAbQLgM4buEVsAtA2XiFFoHe4lEN+\nNRCAbgOg5TfFuIEB0EkuD/SwbDHQ3fu9bX8/gE4DoLnsDPSuZgPodSXEAqDzBjzQvdAloPe4\nTlN+NRCAbgOg5TdFAO0CoPMGAHpdADQXAL05ANqlDDR7bQKABtBZADQXAL05voGd+WygQ0pI\npgg0f/HYJYDuF24a6G4UB7QB0CcKgJbfFF0Da8cf93t4CdEA6LxBQ6Zbyt7nZUDjMrsTBUCL\nbopN3ABAA+i8QdMdETufAfRcADQXAL0lADoJgM4bAOh1AdBcAPSWAOgkADpvYEpAWwDNBUBz\nAdBrksgCoF0AdN5gE9A7bD/yq4EAdBsVQBe2p3MDHd7AGzcA0AA6bzAcEps1QJsdNiD51UAA\nuo0GoEvbE4A+OEr3yIsDbWKgh+/GQBsA7QKguQDo5fEXqjbtgtuFQNvShHaL0j1yEdDNjj/Q\n5NfDUqBtGMEBPRxjA+jzBEBLAt0u+bCn0RzQYbx4QgW1t0XpHrkI6D1/5ZBfD20Dt8EyQIdD\n6DHQtMuvYPKrgQB0GwCtCmi3NxYeVAS6NHBblO6RAHo10LusD/nVQAC6DYCWAHpYYLMc6AZA\nj3NioMOSmeHTSGaBNgAaQPMB0MvjThJuBDosDYB2I72wwtEZgI78deeVJ4E2/uP8AfSJAqCP\n3xTdqzj2WaCbHOgn1prSPXIB0M0pge6f2QA0+YvtPNBhBEMAug+A5gKgFyfapfyO1sb/0c/C\nClkE9DN/SUPpHrkU6BO9WNp9NlIAOtpMcqBtuEAaQPcB0FwA9HziE4u0CugGQBcSA32eUz0d\n0FQA2i4C2gLoMwVAA+guSvfIaaC7wScEujHLgLYs0M+uDvnVQAC6DYBWC3RGbwloc22g++En\nBDo+xbwR6CfXh/xqIADdBkAfCnR45Z3mgE7sLQLd5DsigH5FhaNjugUys0Anbx0E0H0ANBcA\nPZ/4pXlaB3R8RZ17g/NoR7wM0MbfSacD2pvsziYzQNMM0M+tEPHV0AZAA2gBoN3vpAB6lIVA\nu+/PCrTbMAD06gBoLgB6Ph5ocrtUYstaoI3JgX5itSndI68NtNtMAPTSAGguqoGeuuqoDqBN\nY/0A44YB6AsAnbK8Auin1oj4amgDoC8CdGkGaYVjkgLt7PG70gTQ8S7nlqYAtAHQ+1c4OBnQ\nMcs2uQWgCwHQXAD0fF4N9ORyzkTpHnlRoCkCOmWZAdqdqgbQJwuAPnBTNDHQdh7osIuVgPb7\nYzzW5m5K98hrAk27AP3MKhFfDW0A9CKg722Gr1T42gdAL6mxEWi3X7pv/MAR0JuFVrpHXgbo\nYYPvUG5WAW2HD1MKQO9wCK10c5jNJYGOvtzHX4cA6CU1RkDHuGwGOv54963llO6RFwPavQdl\nAmjrgSb/jkITEgP9xCdyKN0cZgOgAfQzNay1W4E2ADoaGH1tRu+o3LfCMWnSv4rSLVLzBNDE\nvwFzSZRuDrO5IND3+KtSoGfGVgW0SV9yD7g0CdDuJGIzPJIB2gDoSwBtAfSiXBFodwqaiAP6\nvzafm/PYkEbDmlVTmBm7NAOB+N2tv9l92w/s7m7cnV3fbjf87Bat+XRAu8kMX7qhn2HxjZIF\n3THROksGRl8HoCXa7ZL+2Wu6LwPQw3KbSaDbsUtAf7oN6Hxbw3yuCPTwD46gn83WI+imeARt\nhjMljwOp5Ah648khpYdM0TpLBkZfaz+C7p+wwhG0e9Y3HkE/8/uU1s1hNlMM3b/9+uhufPz6\ndh/ffbvx38llYQ0AvUNKQFtTBtqyQLv9zgMdzlV3owHonSu8OmuBbj8SEUAzmWLodrt97258\nv5X4BdCFXAFoX86431vHQHcUGw5ot+vNAG0A9CsqvDoD0N2i+A3CAT06bh5WxEKgz/aSxGym\ngX7rvbq/VQz0r2+Pau//wgCc4ngyC4C2Nhw00Qhov+sBaD/Q33kWoLtlGgHdLAPabSIAehro\nn7e/j69/H19b9z4eR9Lfu5MeH++3bz3JX+2wL1IL9NfjZ8uj2q1bkD736D8AvSHPAh12PRZo\nv48D6P0rvDrRbwMjoMdnnhcDTQA6y0O128/H1wfTLb9f99a6+9dw61tHcjfsjdQC/f32o632\n+/YehnHvIFT0TsLzAx1eTATQ5wI6ejojoK3/oRwGrQParAF6tNEo3RxmMw003Vt7324dvz9a\n5N4f4HW3vt7bYT/7b3+pBbqt5f5bFwDNJb7GYiXQdjPQq71SukdeCWizHegmAtoC6HIeqH2/\nfdDH7Xvn29vj9uObN3+rG9aN+A1ADzkE6OkNdd9NseBECeiw/y0DmnigHzu1CacxhzvtarCU\n7pEXA9q8HOjyrnIVoP88Do5/3X5HxuW3+qgFejjF8WO4HmVFAHSbEowLgTYTQDeTQEdeuXvr\nAHoBC9cC2rhfrMZAE4Bekhmgv27v9H77qhfo/sT57Xb/WDuhfYFe+df1TgC0XQO0ezfLtYE2\nZwHavaLnNoEC0DQDtBfaDg9eBfR4dzsp0K3O7ann6VMcbmQNGdX4+Xa7vf34Wj0hAN1mAuim\nDHT6Wv0I6GYZ0PExtck+S3pZADRX4cVZDHT/UaQx0DQBdNia0hT3rOsA/ev2rb2SI32R8Oft\n/Yve+2GPb387wjVE6Qf27wZ0QwJAp1jsADQFoP2BURlod2gFoDdGMdA0BbTbMAA0m9bcx3Hy\n7V9/s3SZ3XAG4R+AHnJKoDMdU6B7VGzY/WaA7j7SjMZAu38KQNtrAW3EgX7ms3HD08kD7T/Y\neQpoOwa6JHSyZzWlgV3OCjTdb3d3M3qjyjf3RpV22PtfAtBDADQPNFn/0j2tA9qeE+j447GH\nL8ZdAiwL9BNC50C75z4Bevx5sjnQ9BzQo9HOCHSVyV8k/B5ex1wXAN2mDHT37RKgTbzfFYFu\nGKDdSY8TAx2WKSzvCOinnZYD2proQ1cSoJP3OsU3CkBT2Jaik9dM1yafrA+AVpIM4m83AP1M\nikD330dXQj0BtB8JQJeAXr/c8xXm0zxxkiMCunkOaMsBHa+UJlnr0S93WS0ArSSjN6r83jgh\nAN1mAmjv8xNA+7+XxQFtAfSTnc4OtAHQVSUD+m3zOWkA3YYHuttjPCZjoD3ftBJoC6Clgd78\nVxLIv6bQA01bgaalQJv4w1oaAK0+GcgfWy6B7gKg20wCTauApgVA+1cWA9BbhQbQXIXZmM2f\nUEUzQNvlQNvFQId9we1lhR0EQCtJfsT8+1znoBvdQJOlHOhuKmHHWgC0fxyAFgN6Yvta8GDj\nPwsLQMcB0Kd/kfBQoJsy0GYCaBoBbYksgPZRDnTy3s5NeQpoNwpNAW0BdMU5+YuECoAOIi8D\n2nqg+z8cuw7ozSehATRXYSI2vPy7dX6vA9pyQPupAWj9GR1Bb50QgLYTQNvNQJsJoO3lgLZu\n4FmAds/nNNDJ6NGNSaApAjp+j0/oCqD1Jwf52/fVn2PX5/JA2/YNX8NZiRVAR/eHfTIAneqb\nAm0vB/SwVAB6K9A26Qqg9Wd0igPnoDdmHmi7FegwmrMZQFMKtDkR0ImxDNDRRuB/bRsDbf00\nXGEAXVkA9H5AmwLQzUKgjbtcbhPQNgy6ANDRD6TzAm1fArRJugJo/dH6YUnrNngVQD/m0hjl\nQPM/9wA0V2Ei5wC61B9AK4lSoFdu8VqA7qBYALR9FujspUXrqKoK6CUfcnlaoL2NtAZo8vMp\nAD3sNRnQySQSoBtqxgOHAFHgwsUAACAASURBVGglyYH++qHiL6qs2+L5EyICQCe7lG0iYl4M\ntAXQIkCXfJtPGeiI5TLQ6QV3GdBNutX4wwKbHHf7ss3APYBWnPyt3kr+JuFJgB4Oa8wyoO0i\noC2Arh7opvv8C9odaF8qBjrulwIdNi0ArTWjv+r93v79xHfpv+oNoIeHrwC6HzQDNLumADRX\nYSIx0Gtm3ETl1wHt4x8EoOOcHWh39cbRV3Hk22DtQHsuzBhov/utAjocJHugqQT06LTjeH28\ndDWsyKmAXjZn9/FxZMJm8RTQ5N4YVQCaAHT9AdA7bIrd7MMhjQ1vm3B6zAHtHQLQadQDbWNf\nZ8MBPZyesuuBHmoUgaYcaDsC2q9PAK0zSk5xnAroiItngR72HRsD7TWOzplsATpdaeqBDr+a\naAV6wawd0MmfeA/H4DHL/T5guUUC0MWcHWipFwlfBrQ73TdT4bkwQNsJoK0vtQBoa+0U0BZA\nVwN0M3zhgA6L6vYBHujg7hzQfoNKgHarDUDHKb5Rb+qEwm18M0wgmtSWt/+puczuRUA3dATQ\nTQq05+LFQBOABtCuRhlof/YEQC/OLfky3FoG9G24fSv9E/27oc7zuQbQxRl1s28OADoo3c9i\nA9BhCRoAXUr9QJMN+w+AXp3ngQ5TiKY1muy6Os9HL9CFzW9UYfGc2Nm7bf+lQIfRLgu0PQXQ\n8WZRBrodPMykOKUJoAlAM7HlJON4SYej4e7MxI1u7hD41nMbnbqIHnrLB4xurQV39HGj/Sze\nznEOWhpoUwaawvHRU0BTCWj/tdy/IqCHF3jrB7qJbnW3HdD91pAAbfMPC2ACoIvZH+j++Hc4\nCHYA30oHxW5Y6Qz0XkD/cD8n6rqKgxv5EKCb8JdpjXvRfAZoIh5omgU6mgULNEPVDNDrPkPw\n2ZwD6HBuy3JvVlkFtAXQLjJA+xcJI5Q9zNnX6Et6LiR5bTAfaU2y8e+3v+2Xf3VdB82OfSzQ\ndhpoR6tNO/v9Z7A1ApoAtH6gTfTEMHMfAe06Pw20r7EcaL9xXRDoJRmdfF4K9K3wcH9rL6Dr\nfKMKgA4jAujnsgVoWgm03yx2Atq9n2UWaLcphkkA6DzJVXPRgfQ80Nn1eS8B+tvt+1d7rd3t\nfeV0rgF08WS3v9Z6M9B0FNCN8TtxE93yqwFAvxro6EVBD/Tw5IUlXLIU64AOr0YC6JlsB5ri\nO190FYd/o8q/tRO6LtBmANpGQCenkP1e8gTQ1p8+LAGdfBj1BNAm/ElnDUCPnpXTA23c2CbY\nOQZ6yQcvPQ+0W21+A4wDoGkl0MHpm7833NrtOujhjSrr/3LsZYHu0RMFmlYAbfySiAM9flrO\nDrTxQNMk0AsyDTSFjatfeQB6aW757f4yO0qu0EiATs9tcNdx7PROws25MtCGAdr7/AzQFF0g\nuwfQ/ZSTkx1uNaz8S5DPpnqgG+uuZ58EOvws3Bto980Y6MaPBaC3ZzcdFVR4GdAL0OAA7t7h\ndwTQDQu0k3MB0O0H4wy09nvwALR9BdAmPtnhVsPKvwT5bM4CNM3+lYTXAB12jS1A+62oDPSx\nP6vLAdDsVRz3+9oJXQrouG4/+RLQxqwDenjjQ4zxSqD9YbhZALRbJwHoyfW0fw4Feik4G4D2\n/3JAmxLQQ/EcaLLLGiQrbzzvWaAtgJ7LljMSuyfucL9FWTuhKwGd7AyTQNt5oON+3YQjjM1w\nUDwNNI2A7uc27p8C7U5H+9VQE9CNONDNUqBHT/Uk0AsbAOhiTv1xo78in3+tnRCADrvaJNB2\nOdAGQPdr4FxABy1ToAlApwHQ7CmO9bkq0CYC2s4BTUuAJv/WhaOAtqQbaLfcBKCjqUZLNA+0\nZ3p4JTr63AEArTl4kXDFVtAMe8UCoP3xSmOCmLNA+5PbZaATgncAuh+j8SyoB5pGQJsR0IzQ\npwM6XiAA7XJ2oOs4B50POgzoYULx3sAB7a69apoy0GSSKYyX6EmgzRTQ/qKPbqkcC9Praf/s\nArRf3G78Q4FuAtBe6NKIYb0WgbYqgTYKhAbQewL9uTXddjIe5m4240fkg6KxR+M13fTL969N\nM0yo3RuiebdDk13NRsM+Y6CHQelClPpFQH8mQHdzN36V+WHu3hjo8QL4kUyYxGfjlma39bQw\nc7Nr+nFsP2bXsvunBzr6RLhhWZr0mRlPbN88GoyBLo0Y1mu//m3/fQb051T70uyj23Y078bP\nsJ+bdTPuq8bbwLCpjjovbqIpZwe6z8f7z9UT2n4EbcwBR9D8xaUrfkwbs+wIOpwxbi9OZY6g\n87eXjeY0PCw/gqb8CLo7be3uXXAEHf2x2b5InUfQOdDHH0F77my4zqQ0Yliv/ZNUPoKmJ46g\n3QUgo3uHFeSuqPeNo4+ydUfQafWDN4VycATNnYP+uq0WelegYyouD3T/l50BtDagTQ509CLv\naMRwK/5gjGeATrIIaBsBbQF0HWFOZRx5DvqlQJsdgW480GYaaEqBdmf7tgJNewHtpngmoKP1\ndCzQAdsM6LxC9PwyQNtdgOZbAuh6U4b49+3AdxK+EmjjXubfFehoek7GAtB2BdD5rFYD7Y7C\nUqALqxVAT2cd0GYL0GErUg20vNAAmn+R8MfaCakE2tn5AqCHCc4DbWOgKVz+dgDQRSrUAF2Y\n3QqgTQno0W/66cSW5IxAU/hcGPc2KABdScpA31f7LAk0uzF5O6e2tnUnHXOghxnwQNsU6GYF\n0GE+BaDD/BOg6TxAN9NAh7gt6Bigk8/VWAd0eEj03fCLlSzQrlPyuA099g2AVvFGlbqA9u9A\n8cM2Aj1ZH0CvAdrOA734k1TnNgfLA92sAjpsFTJAu/L9VgaglQZAbwM6AnL0enx8fHIQ0DQG\n2gDofGJLMrM5hOnvBDS5JfJTB9AuAHoE9J9vt9vt2+8NEzo50JaeANq+HmhK790C9PRq2j/r\ngLaKgXZX7WwC2t3hp/5aoIkF2uaP29Bj38j8RZXsD6TMvHFv6gh343v++Ol/vA+TfDvyT17V\nAHQEg3uppx++DGjrfpdVArTfObuhlwB66ZJtB7ovCaD3i+ifvCr+SVh+9LX3LR0rufft9v7n\n8eXv++1t0aTjAOgpoIc8A3TY0bcC3fjhMdDDTOoAuvErogR0wwO9eNE2Ae0/Z5YF2qYPIasG\n6PBd/jBxoQF0/nnQ78Ot9yM/D7oWoIdpHQh04y7KS4GOWJ4EOt9rzw60kQPadeKBtulD3BYC\noCeyO9D5lmMKyzkBtP+LsTf3N7pvheHp348dboUxwl+Pvd3i75jE973f/g63/nqqFwdAzwHd\nncdeB7QbG0AvALq0yPHMlrVaA7Q/ZxR2fQ5oY/u3TUXbRbQZuVUBoJMoA9r9KW/3d717m/Ph\nt/FjR49MJzdZOfkj47fSzYU5LdBOyBzofrhZAXRXHUC7FGY3DTTpAdqeGWh7baCnXyTMZS18\nDUDf/JFzYYy5kyfjewF0If2W/2Kgmea0COjkEUuAtpUATY1WoKPNIVqNw+2sgr9iZgHQ/m/b\nrM2eQIdVvKHIrpE7B30rfzuclBgGzQOdT8Sf2QgH22uAPucpDjOzsW0E2mwDenR8tQjosNP4\nuzmgaQPQpm6grQTQ+ZbAAW2HzebRbwHQCxpwtVYBbQE0l0zNW/bvDkBH87rRGqB/C75IOP6t\n0N2uEWjaA2haDXS62AA6ndmyVi8DerhfHGgKQLteADoKD/QczOuBXnkO+uHye3sMLXCZnXkW\n6NLmafwvoS8D2vuxGOjRpwVvBDp/8AKgw/CzAm3kgR7WejihqwNob3EJaBsB3QDo+Ev87ehF\nwcL3S4He9CJhK3Sf96PfqKIT6HY+uwNdrFkY9hKgB+v8jkkAeqrCOAnQg7EFoKOfx4cAXfjF\njPyUlwNtAfTEVRzusrpb9j1lLwWOgU7GyC6ziy7Lm6ozpH+r958NywWgU6C7m7QVaMqA9q+s\n5w/hgHa/8I+m6ffJMtAH7pSzQButQA/PtGWBjn9h4oCOt3slQLcTuTzQyrL6ag0urwK69CEK\nVQLNz6b0B5RzoGknoMPBcw60X7yjMge0/3lyIqDDb1bJdq8JaAugNaVGoPNBrwK6mQXaLgea\nnUv5Z9AAdHzG+hmgGzcugJ7JS4G2ckD7TdOtTQBdRS4BtN0N6Ah9D7TbnF8CdLaYzwBtKgV6\nuH0CoP0WYgH0kgBoAL0OaBufTaQUaJu8A2v4EPa9gU7uTW4tApoioN0L90PjcwO9nJvy5uCf\niNVAu6WoAOiutQXQqqIGaM6iEtDZSeiXAd1JuxxoonjDPhjo9NZyoG0E9OR62j1LgI7Wqxqg\nmzMDbQG0rgBoditozHCygsIxk9uk+/O5DNDRMrwIaDLpeKNba4G2VQLtT+geBrRNgbYs0GYV\n0MmvLscCPWylvroB0KoCoDcD7XfT1wE9Wkz/kPF4U0A3ZwE6XJ9WBtpIAO3nEIDOnpYi0PF2\n+3qgI3PdKvPDIqCHcubo813FAGgAfVKg3WHSLND+fE0VQEeruzag3fPhb+wL9PgNqn7CALrm\n6Ad6vJUcBLRZDHTUYBPQTPdin+whlQOdze4ZoONj0+K8lrV6Emh3oiB+MuLLfF4GNJMlQLvF\nic7ZAGgtUQ90YTM5AmhbBtr5ph9oirVKgY66KwbaKAK6SYCODjWzJ75qoP1KBNCKAqCLW4Hb\nldIPX7BTQOfNAfRMngSaDCVA+wXj5rWs1cmADks+CbS/ZZI7d22yPgD6/ECTA5oVUifQhTM7\nJwM6gBGyCmg6EGj34Ha1NcHnp4G2AHoiABpA80A3skBPv3C4FmhDI6AJQJdS2hzCeoll3gy0\nVQh0+FUTQKuKXqCDc/mDGnME0MYLS9UDHXa4DGgLoLMUNgf7QqDDWFMNnkhTBtoA6DpSI9D5\noBhom493eaAtLQI67JgHZTPQ4SfJUUCHR1sH7VKg++IDfNRdd24joKN+Uw2eSEPR9pgATQC6\ngpwFaH+EY7PxxIAmHUC7ve9cQNvugUcAbfcEmoiizeEYoN2msgToaH0CaB0B0MWTjuG6o0mg\n4607dIlmvxno0sAS0BNv+vZaDL/mngroHrsMaPfzsjyzZbWyzcE6XodvI6D9Rxb6WYTzF364\nUqDNi4EubtKrA6AB9CKg7Rjo1ApBoHmqA9Ce4NqA9qxJAN2t2RRomwOdnmx2qzya30KgKWp3\nENBhoL/m7wCgV8kNoAE0B7TfVn0mgLZJ3dVAl6/sGg+aATo/7bEN6KmiazO5N24E2ggCbV8H\ndLSqALQLgD4R0P1++TzQw24Z7W7PAE023iOXNYh6TC93Nl5+LA2gs4mt7OyBHh5slwPdPcL9\nFRsAveSOUgA0gH410CQBdONGPzfQ9rVAG/f3GvoH+60AQC+Y6+o7SgHQAJoB2nBA+627OqD7\nR3vT3P17AV28FGXqAU8DbV8L9LC+CkC7FbUYaKsc6DBwWKFloFfgCqD3ytmBDjtvP2y8+3JA\nh/cUVAJ0PmwK6HA/gGY6F4GOZ7ga6G60w4GOlifeSAF0HVEDdLIxzAJt8pEd0BEw3VgZ0AUp\neaBToWOgSQTowudz7AJ0OJ9TArp0iF6Y5euBpsOBNtFfcEmApiVAm+EDUEpA+0cUVhWAdgHQ\neoAumOtv5g+aADq+ZyPQ3ZnHfk/XBvRSBHmgLYCeyRhoOwV0enFjCrTfTEZAu4cUG8gCTQBa\nVbQDXdqxjgLaPgc0jX6nnVgJo+wItFvBrwO6uS7Q8SzIVVsIdHn9aAW6+BTPzXXxHaUAaAA9\nD7QzmgfaMkCTm6VioN0/VQBtjgbahJksAppMOFeuBOi4H4CuLwB6BuiYuRjo0Z3FbrQn0CuH\nLQY6HPxtBjr/BNi5B9CxQJfmxS1K+phsK1gOtD0f0MtWYD/u6jtKAdBLgb53/7QZvlL0tY8a\noG00vN+L7ZNA+32zFqDJd5kD2rhdMSwwP4NJoIuH/Hw3QaCnnVkBdPmizvgt6RUB7Y/6+y+f\nY6ALeyIbAL1XFgE9gDx8M/wTD6MjgS6OHH+mWBje7Q/N00CbCaBpDmjKD7WKK2FRdgd6uPli\noMuPWwq0X5SdgJ5xJgPa7Ad0P5oY0JSsghVA2/D4xfMC0HtlCdB3Ugt0Q/qBJtVAR2vQucPM\nYOIcZFMuUjPQbvaLgSZ/RiMCOn5cP1YtQPtt2tcF0BJZAPSA8T18Wy3QJSmzraAVyzJAh4+J\n1gP0RA4F2hwMtKXMy/2BpnVA+8uezwC0BdA6sgJodwo6GjYA/V+bz61xe2I+yN8qjT/cbvzj\nbX7XZ3czAN0OaneO2TKP0YLJCdCfbhf9HMYZhvV3RhPIMj/bZWnWjT4C+vPTfTPcndx6dHTr\nqTjThp99U1xs94Dy40ZPevH+sBnYYZB7cj6Dl+7PdfV3zcxrcqahbDeaSSaczbB7Xsczsnb4\nkj+uH8NGG8PK5/PJJKsg2r2Gp9ytoxjoobB/1OJ5sUv26kW+IND36L8YZo1H0Ml0zHAEbdcc\nQfcPCib7zbW7Z/4IunicofkIOtyaPYI2bIum8DSFQ+7yoffoSadkTUSl6dAj6CYejQG6eATt\nVkR0BO0fF+aq+Qi6+2OfMdBDYf+oxfNif9vCEfTKzAKdOnxyoJuTA22fAdotmTag7a5AmyVA\nD/OZBjpQVw3QFAM9bNQx0IuF5oFesw0D6CVA3+/R9XTqgG5UAB3t9dcFerTck0Cb/nRnOlAe\n6Gw0AB3qAmiJLL8OWuUpDmM2A+22lBHQZjXQ8V6vHeiwjhigR+ZEk+NajJ7AfkR3MPoSoP2y\nrAPaFopmtaIbOwEdTVcL0OHWK4AuPuVtAPTKrAOaeZGwzZ5Ap3vmBNDGhJeds7teBbRr5IHu\nrxNN55pFFuihqBjQ3T2jB60H2swCXeyf9ZthZjnQdBagPcC0G9D8mAB6ZVa+k7D0tc8ZgG6G\nCawDOpnaFYAe12CAjp7C54H2z4UpAm3ca3evBtq/UFi8qt6MgCYe6HKkgCYW6PElrPOzYu4B\n0Cuj8rM4pvcnk25fbr/N7poHugkV3CDlQK9MX9yhZtYD3d0sAZ3vZfkTmDygu+scQHdfwvYG\noPlZle8of2YLFwANoBcD7aZWG9AeNbMa6L51/Na67kbT5IdBoyfQD/YP3A9ox0cM9HBDB9Dk\ngHZbUz1AJ+9aAtAaAqBjoJ1jJgba75Y1Ah0WoV+maB2Z7NZCoNuPFh0DXVrweOpXAbpx68K6\nPxU7jOVmqhloAtDqogzo+F2n4Wb6GJNuX26fHY1tVgPtilwdaOtrUxHofC/zKBUGywKdbCfJ\nYvDrLKy87PKQGGjLAB3WRQa0WwEAenkAtCqgjd/i8z0zfUx5v7XpPQSg54DOqfZAu7bd12YE\n9PiERYTSaLAo0OnDk8Xg11lYedmnMEVA29VAu6gH2q/Ufq/xfQt74tSsync0ZPx85gOgKwfa\n769mf6DJ7WAZ0HaYRQZ0NJHxUp4K6Pbri4EOz6URANqPd1qgkx9Dq4BeKCu7jvszQAB6eWoH\nmjyh6eNoDLTNgDahQjJl497MsA3owsanDujoTJK/MQO0TUYezWhPoMPPkXQzCJEGmqaBHsZQ\nBnS0uk0CdBgDQKvLeYA2M0Bbm3xyfuPGTIHuBi8B2vE3WiQ9QIc1686bTgPtj/wKQIe3UKYr\n2U1oFujClXkbgPY/S54CekLoeLwIaBu+vQjQVAR64TkOdsxhGgB6caoHuhlAjfZePxplQMc7\nh59uBnQEbxloG2ZeB9A2vLC1HGjvTw60W9fZfI4BuvFVJ4C24xcEChsU84TE43ljU6CtsauA\nTmelC2gyW4Ce7k8AesfUD/Tjf+GC5aAPgA6nLgLQVATa75PGAd2NWgS6BKtxh9Y2n7ufeA50\nU5rODNANBaApAjosgEmBTh+ebFDcMxKPxwFt1wCd318P0P19BaDnFmAW6Im3EyYPA9BnALqh\nCGj/cuBWoGN4HWuGA3osDJ0MaFsCevRzySRAl15VHAHtppUOTYG2WcHFQEf6qAN6bmMQBdoN\nehLowk6b3MMDnT4OQJ8P6ICHWQ208S+UxbQMLzG6fqcGmqIVtRzo4XszBTR34Uc6dAXQ4V2R\nI6DjTSAGul2kQ4Eu/oYFoE1TvpPyLQJAnwDo9gzH64GmywPt1roZAW1ToJPr8oxvMX4Sp4D2\nT0MCdJNsGr5vtACjTcBE5a3fUp4Guj8NW5zIMIcrAV38aBauQmlrKFRsA6DVA20Lz2a41xwN\n9LDb+enzW1oSAF16EtcDTfGT74bPA21fALQryq30EwFt4p1y2AnSRzwNNPM2LwCtEGi/u0W7\nVvqY8AybHGj7KqBNPLkwfW47zDKzSx4ANA03KAc6GpEBejhcdWvdTANt7euADosUT2YGaLMK\n6GSOLNBhyasCOpxZCL3MLNBujPDE50tQukIHQO8UTUAP1ynbsBeuA7ppdgI6YWGYZjS5MH1u\nO8xSM9AmOUtQBDo8G/26jufuW5SAHq2/FwJNvZrGD3PnKcZrLBQMlzKbMwBdcNAsAtp953eC\nZLkA9AujD+hw2DIHtLvH73YrgA6vsK8COtq9ooFzEQU6XO8wDbQdA20WAN1kQKcTHQPd+Dsp\n3x+PBrrwtMTzsecFOvkDQBuADs9BQ3sCnd0DoJUDbVcBTQWgwwQToOPpZkD7XdjNyQ/KgI5H\nnIkaoN3AZUB3I8b75AKgTTpR04Tndxi/iZ66fP1tAjq+3xwKdPEdGyasdb1Ax4esRaCHHdMt\nMyVAx09n6RPq+B3DbQsAemmUA116Nv0wd8880Ck8Hn7jKvhHlIGOhgHoSaDjddLdzIG2/gOT\nh1EKa6IAtO+arfT4mfL9kwV8KdDsSr8O0IUPN5wGunTMBaDZ6AY63rVd3M7m9057JNAUXsIv\ndGMiDnRE8JNAWxMBbbudfg3Q7rfj8JDCmkiAjhbFT3Qh0G7cPYC2fsprgN7w0YbHA52P1vVf\nDPTwJI+nUKxgykDnz/IQAK0c6GjXDtu029kKQNMBQPuUNjQmJwW6Henx++1lgHZbwwqgC6kQ\naFMCun9cU9oL+D3DFIBuQonsHgBdDdDRRu12NgA9G09FzvJioMPVK84dsxLo5MesX2nhIYU1\nsQLoJl4ACkAn404BXfzrigSglwJd2jMA9I6pH2j/AHLyusMnehZocrtkaTOsDuho4Hqg3e7J\nAB3twf1obu6BtvYhzWKgTSxt1DV7JppwUUgOdLgepwC0X8grAU3LgSYPtIlXbVg3ydORTaO0\nt/g/pzXemQD0VKoEOtpQ+rvcU34k0BPHCXlOBLRfR8NimSLQ/uESQPulDhtP0twsB5rOCrRP\nYRPu6i8HOplG+Dg8HmibXZ4KoKdSBdA2B9q6DWP4RdXvidbtWckZDgAd7xJmR6Ddk7EQaDMG\nOlkzLwfaLYZbSLs/0GGt1wB04WXMrv6TQBfgHz5JpVvn2VOYbIfRQwB0TUC7rdptNguA9rsh\ngI6qehXz5aQC0MGrbUCbALSh5JarEq+aSaDDIiWHX2EBQofkWbO7AO02yrMBPR7W1Z8AOj7L\n5fbDZGrRExzPyAOdHrcD6MloBtqmdwwPcffEQA/P7C5Ax+eW/S6ZseDvrBTo/JZxUibryXPq\nDoa9USYC2mgG2oa+bor+YrlFQFu3Cm2Y7qmAHqerXwY6vAxBfjUtBtr/eAfQK3ISoBsTnY62\nfrQU6OHPxl4NaPeKXTQ0v2WclNFaWw20u3vYCx2KxstM/v5JoN0K54GOHvJioCkC2vqtYcla\nPwHQ0dqk54F2+3IZ6HDyOnoIgD4P0A5eBmiHyBzQ8TV7dBagh5vR0NKtHOj4NVrjnevXoxmA\n9uLyQBtTNdA9VwA6Bzqcjl4ItN+XAfSqqALaxX3r7wDQm5IuSTS0dGsCaEdazBcxQMcjD29j\n0AG0uy8531UG2gDoA4HuBgNoJtUDbY8Ausm2HH9nNUBHr9aP1UuBNt0nvi4H2u3B/gW1gOJW\noGlfoH3pJUB7dEZA+0PvRWtdIdDL0tVPgXarbw7ophkPi6Y6PDHpvf1g98jkcQD6XEC7535X\noOkkQCdDS7esf4Tzya3+JUDbItCJzAWgg4PRmtgF6PzERrgvBTpZPf68DAO0Nc28r9UD3a2A\nZUDHW0ObpnH6jja8aCePnk1/B4BmUjHQ4REAupxyw7F6OdAmBdrsCbRdBHR4/rOqw/ZQWtIi\n0O4wOtxn/c8bV9LFRt1MEWi7FGg6PdDRiYywEht3xwjoaEsJQIdNA0Bz0Qx0uCM+o2e2AN2Y\nFOiw2y4CmsIgikcH0P6pC+99nwTajoAenXTcB2gzDbSZBzpMObpecxXQxbvPDLTbbNYDXfqD\nkwCaagHa7R1kU6BpE9A2B9ofK+V/I8DNolKgi7WXAG3MgUDne2QR6OQTKWeBTn8LD0D3TVcB\nHW1mALoAtB1tRtn669LE+3IR6PC5h+FRAFo90Nbj4PaOZ4E2I6DdHmMA9KuAJuP3561Ax5/p\nvhLoULpvGl1oN8ygn2BUGkAPN/xzHp67ALQNa90/cgXQJg2ALkU70HYB0LQCaONPY/idE0CX\ngY74NWWgw16VAD3i0X0gjomBDvPL1kQAOj3ADYtUBNqWgU5KmzLQw/NjRwfdbiUB6I1ARy8c\nhZ2cAdr/ouUDoGsCut+1or3f7zm0I9DuUyr7em4WJwV6/LdDo91lR6DdThx28mR+oVoMtPdy\nvEgA+qUxEdBuRwvP3bDySkAbEz/xFK2DwC+AXheNQCd7WYRDuHce6OjAex3QCRpuFqcCuvR3\nmBpjnwHaOvZ2BNo5XVgk3UDnOGW5GtD+bLP7Uc4CbfxTNQRAawA6JmE10G5z3xvooZ7bOUfn\n1Nx4+oEuDC28oayxa4G2GdB2DdDGxD8Q+grt93sB3YQneArofgnsNNDNsJUB6E1A+80gBjo6\noh4nFAHQuoCOLk49Auhw+ASgyS4B2p+e775vJoFOUKR5oLsCDmgHKLPWtwFtnQ/J9JMXOHpx\nQn23ugD0VqBN9J3bdwypKQAAGuJJREFUx/2Uy0iHIgC6ZqCH/W8h0G6PMwB6Cuj495n0ZgFo\nv/OpBtqXZoA2OdDxr1fD6gLQG4E2xkwA3QDo2SgD2lsctgQTfr3mgaYVQJtoImQngSY/B4aK\nUwLdXxPl1nF4JjKgw843C7SNgbZ+2LAHhwJnApqY0WYfrxFoywNtM6D9E+/Xvc2AtiWgw81Q\nBEBrAzrdCqItIQDtcRgBHZylxUCHHS8AHbPQAOjwTFjPqVt9xmTv+siBdjvlJNDGF3g50DYB\n2ngyBnqTY/xodW0Cmsk5gfZvBCwBHf+0ToGm/CNpDYBOUxvQlO1DOwHtdm4KU+gyBXRyqD2Z\nCoBurH+Eid5VkDwvBaDzSyImgU5c7NdJAWh/ILsR6I6LEtDu50P8MqYjA0BHMRnQ6empfYFu\nkrlkH1MKoJUBHemZbQmzQCdnKmgr0H2p8c5JVLo2Ld6LJ1MD0J/+EQuAdnunA5o2Ah3p6YB2\nU9oMdPuYMtD9CbTVQNNaoJvJraJOoEe/dGSnr6aANhzQFkDPRivQ0ZYQdprw3TqgyQOdz2I5\n0IVkezGfyoAOT8k80PYZoONJPgc0JS8+EZWBDshGmxgHdDyTlUBPfjD+OYEOO1d44vurGMMw\nv7YB9PLsB/Tnxpg0I6A/w04Tvhvufjy8HfbZf+1vDYNNpO/wvZtZCWj/wPjG52fTT5hvvmgR\n2Sm8OuWCzcSwbpkadxBdAtqP5na3dlgAul3a4SF+xHbxIwz9M+u+a0dMnsdhzMejSotkCmsz\nPIf+ibahjZ9FP5pvGDrZvkHY1pKZRJsJvzmEdVlawfG0Zh4vncatdbc2o00g7Jb+Gf0ctrOw\nDw+P7TemsDH4te0fm8/FMFvs8gBoLi8+gnbf5kfQ4YDEHdqY0hE04Qg6ZPYIunEvr08dQfvd\nzfBH0DY5gjYZ0P2lN/5pLBxBlxepdAQdnkP/RLspu0H5EXS8DMOxsel/1ph8JtFmwm8OYV1W\nfgTd9p8+gna/bZjozBKFdRoeGwZbf3oxOYImHEFPB0AD6G7YUKI9dF4OtBtIyb0e6IBxEWjL\nAR1ezisuEgN06EX+dS1y5ziGcTKggxljoLOpA+gJoP3LiH79j4G2S4B2J0j6AGj1QMcfAG1e\nC3TYNkwCNL9H5bsxn+ldUhPQ3UNYoP06iri11tAs0HYENKWrPQaajgN6WDJ3Gb1hgPZCA2j/\n5Pl9aRizDLQF0M9FO9A0B3TArwS0f+1wFmhbBDqa7jjNYqBnV8KL0phlf8g5A5rWAe2uQ3Mr\nLt6Nrwj09F/Prg1oWgh0tL2EIXYZ0NafAQHQWeoH2qcItNuhZoA2MdBUnO44FQA9bUU85ouB\nttEjhqdOAdDNQAeATrIC6HTFbwbanWME0HlOBHT6l6tWAe2+HSaU7mDXArpJBTbx3tmuKZvc\nvRzo/BYNK3YC6GLR5UAnbYZxikATgE6zFWi7Fmj3UADN5kxA95kC2l09lgHthw2TuCDQvsRw\nAtU/GY46G4yiMtC0FmiKfnLKAE0R0MOW90kc0ASgOaAtgH5V1AEdvd97f6DdLHYCuvT2wm0r\n4VWZfr2qVGJHoAssh/Xt5psDbeaBLt2TFKMNQLtNAECvBzo8u5NAu33XCW0B9HyqBro4Sf/w\nZIfqBvhZzACdZgLoxfzNrYRXZX+gKb17Dmi7DGjrgO7ANPwp6KVAhxsFoCkHetgYCEB3yYHO\nf+A+BbT/HWkENBkC0HkqArqJd97NQEc2Z3ScEujVJUZAWxZoN2QSaBurzAHtJv3ZT2IKaPem\n7ixTQFszA7TbLBzQSUE3+QsCTS8D2v3cpm5rceukAdCj6Aa6G2dXoIdDOgDNldgPaJsmHsYB\n3cRAM0XLQj4LtAHQIQcD7f/mWJNuGgCaqgDajeF//SUb7X+jAOgoSoG20et8xwHtZwOgpzMH\nNK0BOr3lViGAXph6gCYK/zwDtDVFoA2A7h+xHmjya9k5OAt0tErDSwHDVTbkfgiXsxZoij4U\nbwx0/NrEbkBPpm6g7Vqg4ze0zAEd/zBtA6CVAG2PBtrvm88BvY/PNQLtXuSx0a7lZ2ezhywF\n2rq/gMU9E25O64Am8lfb+DkD6KlwQIdVMwLaLgF6eP1gAdC225IAtF6g4x0MQG/O7kC70ZcA\nTQnRC4C2rwK6iR5r/b2GAHQxOdBua9gEtH/iafjbzguAHr4H0JcE2osDoEslMqDts0C7v8ub\nAh1mPJxuip4JKaANgO6zEWj7LNAWQI+iFGgaAd08BzTxQIcC5Y4AehLo/vsJoCnskh7oaMbh\nNQG3GagAujDTywBNOdBUADpsFzzQyRNPDmg3mRxot7UB6Cg6gaY6gN60yONUBLQffdi//ID4\nvnAIygEdzzh50VYMaBuAjl9VTGZ6SaDJ3WCAdj+5o32rfcBwC0A/G31Aj3ewGGg3EEAvyquB\n9nkOaPM00PFfJeeBDg92d4dTXwHowklwAL0C6P6sVgnoSGIAvSynB9o92QB6YQke6PjStymg\naQJosvn63Ano0GvqV6wi0O3WBaDTPAW032xWA+3f+d9dKA+gNQHtzwSyQMeMagB6r1QDdJTN\nQI/Wpwc6PP3iQI8+BQtAp0CT3QS0XQp0PxMAXRfQFO7dBejwwgaAXgt0d0lr8lpffLt6oIuP\nuzjQdhLo6DocFmgbAW1N+AZA86kGaH/jOaApvrAXQLMlZoFuJqSy7jqIFwFdGAqg9w0LdPTM\npkAHljOgwwuCCdAJywWgDYBuowvoCModgKbotFd0AhtALyhxPNAhuwBNxScUQC8MD7QdrtJ4\nFuhmeFkDQE9GLdDRDmaHPXs10P2jAfSGEiOg8w/HmAGa/G7sB/T7+BzQzdRT4aY1DoDeN30J\n/0eHY6C7Qemx9Dag/UMBNJ/zAR0umhoeHe+S/RZ1HaCXpwQ0Rbtanjmg/W7sBiwB2ho79cz6\niY/zJNAEoNMMQJMg0AZAU71Al/c/dw8LdD9gDLQ1/PQAdHHVTAPduDcV9uNYWgK0dZAfDzQB\n6CQloOlFQBOA5gOg/fETgI6yM9CkHmh3DgxAdykATeuAdq/Tc0BTDnT/TwQ081xMBkBzeSHQ\n9HKgCUDnJZ4B+nHAXAQ6nO+Ix90d6PxWqfQYaJpCAUAvBNoWgPaXVDmYKXwZAd2P3M6vwRE0\nKQDanwIuAO3GssYC6BenCHQ4Aho/YFqqFUAHobtJNkqBpisD7V5ft+7VBXJnIwqH0M8ATR5o\nC6DbSANtFwFtAfSr83Kgw197TR/2KqAbpUDzfytmiKbNoWGB9sMA9EujCGibfgw0gD40rwea\necCrgC5eTT0COtqmZoEmS3sAPRdNm8M2oP1msxRody8R+Z0SQHfRBLSdAzo+P7kd6OHjJAF0\nkp2BpnVAWzGgM6qZJyPM9OVbg6rNoQS0z2KgG0MbgLYAmhQA3T0VzSagmWnOAt1+QwA6jR6g\nJ57afJL57AD0XnFAu+/XAD0MIneju6THjzA8JHokAWg+9QE9DHsOaFoB9OxJw2ejaY/02Qfo\neN0tBtq/f62YxUCPPpKOAPTibAa68Vd2kGeZAPTmAOh5oF8dTXukTwS0La6ZGaAXPyAHOr52\ngJnM1FxmD78B9JJsB7ohAL1jADSA7jIFNAPrnkCTAND+AQB6lCVAD7+ivADoflsA0KQZ6Og3\n1JcATTHQs2+PeGU07ZE+BwLtLt9xczoeaH8DQA8pA50tvX+dAUC/LDqAphLQYS99JdDJ4ZNM\nNO2RPkcCbY8HmgD0ZHKgw9FyNFIJaHJAR/eNgKb4XgA9FWGgmxcBnZ4f8Y+dBnrTEuwQTXuk\nD4Auz/SqQI+vygkvBPNA58fS6eMB9HzqApqWAJ19ovAyoGd27JdG0x7pE046ngzofDwAXcoh\nQPcf1w+gp1IL0MOtJUATgN6Q1UCvpgpAL4umzWE70BTdl4yUzgdAz0Qx0CHhaW3CRa47AM18\n9MfR0bRH+kgCPfl3YF4GNAHoEAbo4nsCXgJ0+y2AVgO0e9fRHNCjl5VLAdAbIg00mcbPCUCL\nZwT0RFKg+0HJfWGkEfABaHcLQCfRAjQBaNmIA90IAU0AupBVJWxkdH6XjfbuwqpLj68JQOcB\n0AC6y+uBbvjpAOgoKjeHmQDoV0UF0P3t/hfdpUCXPmnBjcMCnU+1G9HfvWkJdojKPXJ/oLkH\nOKDDr8P6gE5+Z5+a/Q5RuTnMBEC/KhqBHo1VBJrfi7MPrAxX6AFoPjzQE7Cum4VSoJtI6vk/\nVAqgi+m2k8LKAdBPZhnQ9+6fR0pf+xwEdPRQfqrFiRiTfUiaHYR2gC8uvXd07pHurb0nBTpc\nDxR/5jGAHrIF6NLKWQV0d8uEa18B9EKgO4h7lMdfh6gH+iHOJNCLXrB+SXTukf5vg5avrXoR\n0GHWK6fi0kz+oI2ALvwu1m41ALqLHNDRC0MAehnQdzoF0Pn7HwagLYBuMwV0OUqBXvjgEtDt\nMADdZS+gCUA/lwVADxhXBHTx74UWgbbm9TvcbHTukZUCvfTBJcgBtA+AVpJdgP6vzeeW9ED3\nt9tXBT7b52Y0VnfP6KFTkx1Pox2aPsS6LG57qXQra2r1rF5zzAOG56AJM5t6ah/jT89l8sGh\nQlMYrzSMnwISpV8thZXjBjG72jAs3DsAvbXHBYG+0wuPoM1LjqCZ33ObwhH01CHiUdF5yKT1\nCHouOILeI684gi6/T9zdmxxB200l6IpH0N7hVwBtouvc1gI9FeZEJIDmIw40Aeg+OjeHmSwC\nevLhALqYeaD7nALo0VQBtA+A7gOgu+wO9PSfXgbQXJZfB10T0It2cQAdZz3Qq//a+WKgnwqA\n3iO7Ab1sKwHQXLQBXXyjwWt2CgAdZwPQa6MKaC4Aust+QC99eAy0BdAuou8ktAC6jc49EkBv\nnMKz0bk5zARAvyiin8URf5ocgJYNgO4DoLtIAD3cAtBxFADtn9PuBoCWCYDuA6C7CADtbgHo\nOJqA7gKgZcICveM8ytMC0OsaHBIArSQAGkB3OQLocgD0ugaHZBvQqy/siR4eXonyH78AoAE0\ngB4y95dEXhcAva7BIdkI9NaEhz9uNQA6RBRosxDozT+YJwOg4wDoPgC6C4BWkjqAfkkAdBwA\n3QdAd5EE2n8DoFUAPRq2S5/5AOg4pwF6bl4zY8w+GS9fIYo3Bz4A+kWRBtpmf4cKQAsFQPeR\nfzLkGxCAVhNxoC2AVrxHHgr0AXMD0AsDoJUEQAPoLkyJA1YOgNbWgAC0msgDPR62R50FAdBx\n5EoAaG0N6HCgw4EAgE6jDujpv8q8ZwB0nGsAPf8bgfyTId+Ajgc6nhCAjqIP6MP+urYWn+vc\nI/fLoUDPRv7JkG9AAFpNADRM6AKg+8g/GfINaEOJvZ45AJ1G9q3eBR8BtEwAdB/5J0O+AQmW\nANBp1AH93B+kWz13mDAEQPeRfzLkGxCAVhMADRO6AOg+8k+GfAMC0GoCoGFCFwDdR/7JkG9A\nAFpNADRM6AKg+8g/GfINCECrCYCGCV0AdB/5J0O+AQFoNQHQMKELgO4j/2TINyAArSYAGiZ0\nAdB95J8M+QYEoNUEQMOELgC6j/yTId+AALSaXBxomOACoPvIPxnyDQhAqwmAhgldAHQf+SdD\nvgEBaDXRB/RhAdBxZIH2t8RauMg/GfINCECrCYCGCV0ES4TnQP65UPBkyDcgAK0mAFoehWvv\nkTHQCtaEfAX5BgSg1QRAA+guAFpLBfkGBKDVBEAD6C4AWksF+QYEoNUEQAPoLgBaSwX5BgSg\n1QRAA+guAFpLBfkGBKDVBEAD6C4AWksF+QYEoNUEQAPoLgBaSwX5BgSg1QRAA+guAFpLBfkG\nBKDVBEAD6C4AWksF+QYk/cZSAO0DoAF0FwCtpYJ8AwLQaiIKNAHoNhffIwG0tgYEoNUEQAPo\nLgBaSwX5BgSg1QRAA+guAFpLBfkGBKDVBEAD6C4AWksF+QYEoNXk6kCTld8f5BsQgHaRryDf\ngAC0mlweaAX7g3wDAtAu8hXkGxCAVhMALb8/yDcgAO0iX0G+AQFoNQHQ8vuDfAMC0C7yFeQb\nEIBWEwAtvz/INyAA7SJfQb4BAWg12Q/ozw1pn4stj9slojNHQvA8ICH2qf0SQHOp7wiacAQd\nBUfQWirINyAcQasJgJbfH+QbEIB2ka8g34AAtJqIA73X/DfPXX5/kG9AANpFvoJ8AwLQagKg\n5fcH+QYEoF3kK8g3IACtJgBafn+Qb0CyJfxGoGBNyFeQb0AAWk0AtPz+IN+AUEJPBfkGBKDV\nBEDL7w/yDQgl9FSQb0AAWk0AtPz+IN+AUEJPBfkGBKDVBEDL7w/yDQgl9FSQb0DSQG8vAaC5\nAOjNkW9AKKGngnwDAtBqAqDl9wf5BoQSeirINyAArSYAWn5/kG9AKKGngnwDAtBqAqDl9wf5\nBoQSeirINyAArSYAWn5/kG9AKKGngnwDAtBqAqDl9wf5BoQSeirINyAArSYAWn5/kG9AKKGn\ngnwDAtBqAqDl9wf5BoQSeirINyAArSYAWn5/kG9AKKGngnwDAtBqAqDl9wf5BoQSeirINyAA\nrSYAWn5/kG9AKKGngnwDAtBqAqDl9wf5BoQSeirINyAArSYAWn5/kG9AKKGngnwDAtBqAqDl\n9wf5BoQSeirINyAArSYAWn5/kG9AKKGngnwDAtBqAqDl9wf5BoQSeirINyAArSYAWn5/kG9A\nKKGngnwDAtBqAqDl9wf5BoQSeirINyAArSYAWn5/kG9AKKGngnwDAtBqAqDl9wf5BoQSeirI\nNyAArSayQJOkzwA6DkpoqSDfgAC0mggDLboxAugoKKGlgnwDAtBqAqDl9wf5BoQSeirINyDR\nEgA6DoCW3x/kGxBK6Kkg34AAtJoAaPn9Qb4BoYSeCvINCECrCYCW3x/kGxBK6Kkg34AAtJpc\nGej+GhL5/UG+AaGEngryDQhAq8mlgVZSQb4BoYSeCvINCECrCYCWryDfgFBCTwX5BgSg1QRA\ny1eQb0AooaeCfAMC0GoCoOUryDcglNBTQb4BAWg1AdDyFeQbEEroqSDfgAC0mgBo+QryDQgl\n9FSQb0CyJfwH9ABoAK2hgnwDQgk9FeQbUL0lADQXAF1xA0IJPRXkG1C9JQA0FwBdcQNCCT0V\n5BtQvSUANBcAXXEDQgk9FeQbUL0lADQXAF1xA0IJPRXkG1C9JQA0FwBdcQNCCT0V5BtQvSUA\nNBcAXXEDQgk9FeQbUL0lrgj0/RH39Z59H8YC0BU3IJTQU0G+AdVb4oJA390/9/R7P7wPgK64\nAaGEngryDajeEgAaQJ+wAaGEngryDajeEhcEuss9WAygz9eAUEJPBfkGVG+JKwPtTkG778l9\nQ/+1+UQQBBHNJYEuw4wj6PM0IJTQU0G+AdVb4pJAU3J+A0CfrwGhhJ4K8g2o3hIAGkCfsAGh\nhJ4K8g2o3hIXBJo7tQGgz9OAUEJPBfkGVG+JiwPNvEjYBkBX3IBQQk8F+QZUb4kLAj165yDe\nSXi6BoQSeirIN6B6S1wR6GUB0BU3IJTQU0G+AdVbAkBzAdAVNyCU0FNBvgHVWwJAcwHQFTcg\nlNBTQb4B1VsCQHMB0BU3IJTQU0G+AdVbAkBzAdAVNyCU0FNBvgHVWwJAcwHQFTcglNBTQb4B\n1VsCQHMB0BU3IJTQU0G+AdVbAkBz+Q9BEEQ4e3mmJbsBvS2nW59bgpXggjVBWAkhWBMAWkOw\nElywJggrIQRrAkBrCFaCC9YEYSWEYE2IA40gCIJwAdAIgiBKA6ARBEGUBkAjCIIoDYBGEARR\nGgCNIAiiNMcAPf4jLHdKvy/cebasWQn3e/r3as4Vbk3ENy67OVBhJVxzc0gW+uybA5dDgB7/\nGcP7PR5O6Tfn3BRXrgQ675bIrYn4xmU3ByqvBLrg5nAvjHTWzYGNDND3eIVnI7k7z5Z1K4HO\nu0OyayJ56q+6OZRXAl1xcygCfdLNgc1x56CTn5Hxb3Hx1/Ezc66sWAknXgttSmviHi30ZTcH\nZiWceC20KayJe3b/+TeHUgD0ocFKcAHQhJUQUgI6OQWd3XmZHAb0nUpr+WJPAVaCS2lN+GFU\nuPOMwUpw4dbEBY9csggDTdd6CrASXAprIv299gprAivBBTsGl6OAzn8mxk9B/6vMBZ6CNSvh\nrOugT2lN3IeLyS69OXAr4azroA90YHMQ0PlvLpf8JWbVSjjpOuhTXhPjGxfcHMY3rro5XEwH\nJge9USX6ctmnYN1KOOc66MOsifGNC24O4xtX3RzudKXNgcsx10G7F2Sv/E7ClSvhlOugD7sm\n4huX3RyouBJOuQ76QIep4LM4EARBlAZAIwiCKA2ARhAEURoAjSAIojQAGkEQRGkANIIgiNIA\naARBEKUB0AiCIEoDoBEEQZQGQCMIgigNgEb2z63L/cdHOvjX7Lt0wxi3wpZZGoYgZw42eWT/\n3Fz+ZIPnHzg1LoBGrhZs8sj+6SX9+H67f40Hzz9w270Icr5gk0f2j5P0++3n49+/39rTHf1x\ndfQt0c/77e1Xe+Pr++32/cuP4SZxu318G0b9eL996yfrxv12+0f07/Z+9LIhyIEB0Mj+ccx2\nfv7pz3b8GPj139KP7kYr9L298VYA+j6M+tXe+Nbd6cb9av95b5VGkNMGQCP7J2H27fa7pfo2\nDI6//aC/t/vjSLrn+ld+Dvp2e/+iX+0YPx7Sf723w8K4P29/ft9+yCwgghwTAI3snwRooo8/\nP9890OHb++17/yLiWzf89m0M9Ac55B+3Pvpbbtz0A90R5IwB0Mj+SYF+709quMH+2z/32+2t\nJzgdwz2y/y6/5cal37f2YBxBThwAjewf5+zf9kj3++3t158Pz2z4lujf2+3+F0AjCBcAjewf\n5+w3f175yzMbvm3zK5y2iB+Ys5yf4uhyf3vDKQ7k3AHQyP4J10F33/wdXuAbgHbf3h+3/vUv\nAf5oj4ffeaB/ti8Xdg8K4/68/fnTXcaHIKcNgEb2j38n4V9yV9MNl83F3/a3fg4X0d3aK+a6\nMYZJxECHy+z8uN1ldm+3L74FglQfAI3sn57gtx+9nt9vt/e/La7dFXPhW/pxv927Q+CPbhi5\nMfpJxEDTxzf3RhU37vBGlW+HLxyCHBcAjSAIojQAGkEQRGkANIIgiNIAaARBEKUB0AiCIEoD\noBEEQZQGQCMIgigNgEYQBFEaAI0gCKI0ABpBEERpADSCIIjSAGgEQRCl+T/X5rgfUfuxOgAA\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "view_dates <- seq(as.POSIXct(min(dates), tz = \"UTC\"), \n",
    "                  as.POSIXct(max(dates), tz = \"UTC\"), \n",
    "                  by = \"1 day\")\n",
    "\n",
    "plot(data_historical, facet = ~ horizon, horizons = 48, valid_indices = view_dates) + \n",
    "  ggtitle(\"1- to 3-Day Out Forecasts: Daily\") + \n",
    "  scale_color_manual(values = c(\"Python LASSO\" = \"#ffd43b\", \"R Random Forest\" = \"#276DC2\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::create_lagged_df(type = \"forecast\")`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 13</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>index</th><th scope=col>horizon</th><th scope=col>Demand_lag_144</th><th scope=col>Demand_lag_336</th><th scope=col>Demand_lag_17520</th><th scope=col>Temperature_lag_144</th><th scope=col>Temperature_lag_336</th><th scope=col>Temperature_lag_17520</th><th scope=col>Holiday</th><th scope=col>hour</th><th scope=col>weekday</th><th scope=col>month</th><th scope=col>year</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dttm&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;lgl&gt;</th><th scope=col>&lt;lgl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>2015-01-01 00:00:00</td><td>1</td><td>4183.850</td><td>4052.930</td><td>4198.399</td><td>19.6</td><td>16.4</td><td>18.1</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>2015-01-01 00:30:00</td><td>2</td><td>3933.165</td><td>3820.782</td><td>3914.647</td><td>19.4</td><td>16.2</td><td>18.2</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>2015-01-01 01:00:00</td><td>3</td><td>3733.846</td><td>3623.968</td><td>3672.550</td><td>19.0</td><td>16.1</td><td>17.9</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>2015-01-01 01:30:00</td><td>4</td><td>3577.479</td><td>3470.303</td><td>3497.539</td><td>18.9</td><td>15.8</td><td>17.6</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>2015-01-01 02:00:00</td><td>5</td><td>3432.463</td><td>3317.998</td><td>3339.145</td><td>18.5</td><td>15.1</td><td>16.8</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>2015-01-01 02:30:00</td><td>6</td><td>3334.179</td><td>3202.149</td><td>3204.313</td><td>18.4</td><td>15.0</td><td>16.3</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td><td>NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 13\n",
       "\\begin{tabular}{r|lllllllllllll}\n",
       "  & index & horizon & Demand\\_lag\\_144 & Demand\\_lag\\_336 & Demand\\_lag\\_17520 & Temperature\\_lag\\_144 & Temperature\\_lag\\_336 & Temperature\\_lag\\_17520 & Holiday & hour & weekday & month & year\\\\\n",
       "  & <dttm> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <lgl> & <lgl> & <lgl> & <lgl> & <lgl>\\\\\n",
       "\\hline\n",
       "\t1 & 2015-01-01 00:00:00 & 1 & 4183.850 & 4052.930 & 4198.399 & 19.6 & 16.4 & 18.1 & NA & NA & NA & NA & NA\\\\\n",
       "\t2 & 2015-01-01 00:30:00 & 2 & 3933.165 & 3820.782 & 3914.647 & 19.4 & 16.2 & 18.2 & NA & NA & NA & NA & NA\\\\\n",
       "\t3 & 2015-01-01 01:00:00 & 3 & 3733.846 & 3623.968 & 3672.550 & 19.0 & 16.1 & 17.9 & NA & NA & NA & NA & NA\\\\\n",
       "\t4 & 2015-01-01 01:30:00 & 4 & 3577.479 & 3470.303 & 3497.539 & 18.9 & 15.8 & 17.6 & NA & NA & NA & NA & NA\\\\\n",
       "\t5 & 2015-01-01 02:00:00 & 5 & 3432.463 & 3317.998 & 3339.145 & 18.5 & 15.1 & 16.8 & NA & NA & NA & NA & NA\\\\\n",
       "\t6 & 2015-01-01 02:30:00 & 6 & 3334.179 & 3202.149 & 3204.313 & 18.4 & 15.0 & 16.3 & NA & NA & NA & NA & NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 13\n",
       "\n",
       "| <!--/--> | index &lt;dttm&gt; | horizon &lt;dbl&gt; | Demand_lag_144 &lt;dbl&gt; | Demand_lag_336 &lt;dbl&gt; | Demand_lag_17520 &lt;dbl&gt; | Temperature_lag_144 &lt;dbl&gt; | Temperature_lag_336 &lt;dbl&gt; | Temperature_lag_17520 &lt;dbl&gt; | Holiday &lt;lgl&gt; | hour &lt;lgl&gt; | weekday &lt;lgl&gt; | month &lt;lgl&gt; | year &lt;lgl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 2015-01-01 00:00:00 | 1 | 4183.850 | 4052.930 | 4198.399 | 19.6 | 16.4 | 18.1 | NA | NA | NA | NA | NA |\n",
       "| 2 | 2015-01-01 00:30:00 | 2 | 3933.165 | 3820.782 | 3914.647 | 19.4 | 16.2 | 18.2 | NA | NA | NA | NA | NA |\n",
       "| 3 | 2015-01-01 01:00:00 | 3 | 3733.846 | 3623.968 | 3672.550 | 19.0 | 16.1 | 17.9 | NA | NA | NA | NA | NA |\n",
       "| 4 | 2015-01-01 01:30:00 | 4 | 3577.479 | 3470.303 | 3497.539 | 18.9 | 15.8 | 17.6 | NA | NA | NA | NA | NA |\n",
       "| 5 | 2015-01-01 02:00:00 | 5 | 3432.463 | 3317.998 | 3339.145 | 18.5 | 15.1 | 16.8 | NA | NA | NA | NA | NA |\n",
       "| 6 | 2015-01-01 02:30:00 | 6 | 3334.179 | 3202.149 | 3204.313 | 18.4 | 15.0 | 16.3 | NA | NA | NA | NA | NA |\n",
       "\n"
      ],
      "text/plain": [
       "  index               horizon Demand_lag_144 Demand_lag_336 Demand_lag_17520\n",
       "1 2015-01-01 00:00:00 1       4183.850       4052.930       4198.399        \n",
       "2 2015-01-01 00:30:00 2       3933.165       3820.782       3914.647        \n",
       "3 2015-01-01 01:00:00 3       3733.846       3623.968       3672.550        \n",
       "4 2015-01-01 01:30:00 4       3577.479       3470.303       3497.539        \n",
       "5 2015-01-01 02:00:00 5       3432.463       3317.998       3339.145        \n",
       "6 2015-01-01 02:30:00 6       3334.179       3202.149       3204.313        \n",
       "  Temperature_lag_144 Temperature_lag_336 Temperature_lag_17520 Holiday hour\n",
       "1 19.6                16.4                18.1                  NA      NA  \n",
       "2 19.4                16.2                18.2                  NA      NA  \n",
       "3 19.0                16.1                17.9                  NA      NA  \n",
       "4 18.9                15.8                17.6                  NA      NA  \n",
       "5 18.5                15.1                16.8                  NA      NA  \n",
       "6 18.4                15.0                16.3                  NA      NA  \n",
       "  weekday month year\n",
       "1 NA      NA    NA  \n",
       "2 NA      NA    NA  \n",
       "3 NA      NA    NA  \n",
       "4 NA      NA    NA  \n",
       "5 NA      NA    NA  \n",
       "6 NA      NA    NA  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_forecast <- forecastML::create_lagged_df(data_all, type = \"forecast\", outcome_col = 1,\n",
    "                                              lookback = lookback, horizon = horizons,\n",
    "                                              dates = dates, frequency = frequency,\n",
    "                                              dynamic_features = dynamic_features)\n",
    "\n",
    "head(data_forecast$horizon_144)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fill in future dynamic features\n",
    "\n",
    "* Filling in future `NA` values for non-lagged features is a bit of a manual process.\n",
    "  \n",
    "  \n",
    "* The features can remain `NA` if the ML model can handle missing values.\n",
    "  \n",
    "  \n",
    "* The feature types (e.g., factor) should match the training dataset to work with the trained ML model. Don't add new features here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "for (i in seq_along(horizons)) {\n",
    "  \n",
    "  data_forecast[[i]]$hour <- lubridate::hour(data_forecast[[i]]$index)\n",
    "  data_forecast[[i]]$weekday <- factor(lubridate::wday(data_forecast[[i]]$index))\n",
    "  data_forecast[[i]]$month <- factor(lubridate::month(data_forecast[[i]]$index))\n",
    "  data_forecast[[i]]$year <- lubridate::year(data_forecast[[i]]$index)\n",
    "  \n",
    "  # New Year's Day.\n",
    "  data_forecast[[i]]$Holiday <- with(data_forecast[[i]], \n",
    "                                     ifelse(lubridate::mday(data_forecast[[i]]$index) == 1, \n",
    "                                            TRUE, FALSE))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forecast into the future with `forecastML::predict()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_forecasts_py <- predict(model_results_py_final,\n",
    "                             prediction_function = list(r_wrapper_for_py_predict_fun), \n",
    "                             data = data_forecast)\n",
    "\n",
    "data_forecasts_r <- predict(model_results_r_final,\n",
    "                            prediction_function = list(r_predict_fun), \n",
    "                            data = data_forecast)\n",
    "\n",
    "data_forecasts <- predict(model_results_py_final, model_results_r_final,\n",
    "                          prediction_function = list(r_wrapper_for_py_predict_fun, r_predict_fun), \n",
    "                          data = data_forecast)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::plot()` direct-horizon-specific model forecasts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Scale for 'colour' is already present. Adding another scale for 'colour',\n",
      "which will replace the existing scale.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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ED/jPLvhxycx5yBUjidZB5zClwSfGrK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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(data_forecasts, facet = ~ horizon) + \n",
    "  scale_color_manual(values = c(\"Python LASSO\" = \"#ffd43b\", \"R Random Forest\" = \"#276DC2\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::combine_forecasts()`\n",
    "\n",
    "* For each of `Python` and `R`, our 3 direct-horizon forecast models have been separately trained and are producing distinct forecasts at various horizons. The first ensemble is to combine the 3 direct-horizon forecasts into a single forecast. The second ensemble--which is optional--is to average different ML models in a cross-sectional way at each forecast step into the future.\n",
    "  \n",
    "  \n",
    "* Below we'll create an ensemble of the `Python` LASSO and the `R` Random Forest models using the strategy outlined at the end of the [forecast combination vignette](https://nredell.github.io/forecastML/doc/combine_forecasts)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IW5F0FzJ6Ebs4JudyskaN4KoqMtIMObY9Ug6An3IGgPEPRu1mZqJD+Bzi3othym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\nT05gRRdDKgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_combined_py <- forecastML::combine_forecasts(data_forecasts_py)\n",
    "\n",
    "data_combined_r <- forecastML::combine_forecasts(data_forecasts_r)\n",
    "\n",
    "data_combined <- forecastML::combine_forecasts(data_forecasts, aggregate = stats::median)\n",
    "\n",
    "plot(data_combined)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `forecastML::calculate_intervals()` - Optional\n",
    "\n",
    "* It's time to make use of the many prediction residuals/errors that we have collected along the way. We have residuals at two levels:\n",
    "    1. The heldout validation window(s)\n",
    "    2. The final model fit over all historical data (usually with fixed hyper-parameters)\n",
    "  \n",
    "  \n",
    "* The residuals will be used to calculate bootstrapped prediction intervals for the final forecasts.\n",
    "  \n",
    "  \n",
    "* `calculate_intervals()` will add a pair of columns to the input forecasts for each prediction interval width given in the `levels` argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A training_residuals: 6 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>model</th><th scope=col>model_forecast_horizon</th><th scope=col>index</th><th scope=col>residuals</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;chr&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dttm&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>Python LASSO</td><td>48</td><td>2013-12-01 00:00:00</td><td>-173.2358</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>Python LASSO</td><td>48</td><td>2013-12-01 00:30:00</td><td>-182.7994</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>Python LASSO</td><td>48</td><td>2013-12-01 01:00:00</td><td>-205.6041</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>Python LASSO</td><td>48</td><td>2013-12-01 01:30:00</td><td>-209.7084</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>Python LASSO</td><td>48</td><td>2013-12-01 02:00:00</td><td>-215.3900</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>Python LASSO</td><td>48</td><td>2013-12-01 02:30:00</td><td>-221.0373</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A training\\_residuals: 6 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & model & model\\_forecast\\_horizon & index & residuals\\\\\n",
       "  & <chr> & <dbl> & <dttm> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & Python LASSO & 48 & 2013-12-01 00:00:00 & -173.2358\\\\\n",
       "\t2 & Python LASSO & 48 & 2013-12-01 00:30:00 & -182.7994\\\\\n",
       "\t3 & Python LASSO & 48 & 2013-12-01 01:00:00 & -205.6041\\\\\n",
       "\t4 & Python LASSO & 48 & 2013-12-01 01:30:00 & -209.7084\\\\\n",
       "\t5 & Python LASSO & 48 & 2013-12-01 02:00:00 & -215.3900\\\\\n",
       "\t6 & Python LASSO & 48 & 2013-12-01 02:30:00 & -221.0373\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A training_residuals: 6 × 4\n",
       "\n",
       "| <!--/--> | model &lt;chr&gt; | model_forecast_horizon &lt;dbl&gt; | index &lt;dttm&gt; | residuals &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 | Python LASSO | 48 | 2013-12-01 00:00:00 | -173.2358 |\n",
       "| 2 | Python LASSO | 48 | 2013-12-01 00:30:00 | -182.7994 |\n",
       "| 3 | Python LASSO | 48 | 2013-12-01 01:00:00 | -205.6041 |\n",
       "| 4 | Python LASSO | 48 | 2013-12-01 01:30:00 | -209.7084 |\n",
       "| 5 | Python LASSO | 48 | 2013-12-01 02:00:00 | -215.3900 |\n",
       "| 6 | Python LASSO | 48 | 2013-12-01 02:30:00 | -221.0373 |\n",
       "\n"
      ],
      "text/plain": [
       "  model        model_forecast_horizon index               residuals\n",
       "1 Python LASSO 48                     2013-12-01 00:00:00 -173.2358\n",
       "2 Python LASSO 48                     2013-12-01 00:30:00 -182.7994\n",
       "3 Python LASSO 48                     2013-12-01 01:00:00 -205.6041\n",
       "4 Python LASSO 48                     2013-12-01 01:30:00 -209.7084\n",
       "5 Python LASSO 48                     2013-12-01 02:00:00 -215.3900\n",
       "6 Python LASSO 48                     2013-12-01 02:30:00 -221.0373"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_residuals_valid <- residuals(data_valid)\n",
    "data_residuals_fit <- residuals(data_historical)\n",
    "\n",
    "head(data_residuals_valid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `Python` prediction intervals - residuals from external validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hf6AKDl0GHP+ED1Xotfc+1qhuHH5idq7nhVR4A+E6eJ6WX+k9P89PXVAKBzAdB3\nnc+FPgBoOXTQMzlQvdfi11y7mmH4sdmJ2jte9VqA1ggMQOcCoO86nwt9cGt80KSyWUizSmo3\nqeSsodNHujMA6FxPBWj9jhIA7RYAfVe4hC71BehsEuKkktpNKjlr6DWSxuOGK91r8WuuXc0w\n/NjsRM0db3IB2roASifFnjAf0n9yXpi/TmAAOhMAfVe4hC4B0EroMwBNdrzp1QAtngWgCQHQ\nd4VL6NLzADqt5Kyh10gaLzlQvdfi11y7mmH4sdmJmjveBEC7ztdpm541/ZkA6KN0jhbOIR+g\n9THqkpFNQhwwrt2kkvOGXiNpPG64wr0Wv2bbVY3Djc1MVP4dnkjT+IBOzwvzB6ALBEDfdY4W\nziEHoE1jANDWvRa/ZttVjcMOTk+0NaD1AHovLWjaMDkkj+8EtKZ9Ab35M6Y/FwB9lM7Rwjlk\nBXRUJaKRAhPRKOkBuXVSurRFf3ayjSEMV7PV1gNsu6px2MHpidr+WelAAHRsoaq3Hn4CoO0C\noBkjBSaiUeQDpCcF0DbnTOgzAE31uwuAji1U9dbDTwC0Xc8N6CxWVCWikQIT0SjyAdJTshWZ\ndl4jaUBuuJqtth7g2lUNww/OTdTc766eAJ2vUpo+yn96XkqAKgA6EwB91zlaOIfaA7omHdkA\n0ohJ7Z5ZizbnbGwAmuh313MBep9fWNppnZ4x/bkA6KN0jhaOasAcZwF9zg6oY5AdXcoGkEZM\navfMWrQ5Z2MD0ES/uw4AtOZPmA/lP20gJeBordMzpj8XAH2UztHCUeeZE10BOh9BGjGp3TNr\n0eacjf3MgE5PGfstPwPQj9Q6vc2+UwD0UTpHC0edZs7sAOjyfOQjSOGS2j2zFm3O2dgHAnqX\nu5r8PO2Anl88ANDsvTbGnzSfbCgAem8B0Hedo4Ujz9KnGgPa0ETrXQjopJCJhn4nccD4QPE2\nWwLGB7iGVcMIo5PzdHS7/9kfoJNDioE/6XlPPh6udX6rfWNGVwHQR+kcLZzjJACthT4TWz9v\n4hMxBtOwahhhdHqi1n7LCwCa1FubMKnW+a32jRldBUAfpWAJuZP0uT0AXZyQrLcYLS7epJCJ\nhm4jccDkgH9/lfTfGdAV/W5/yoTg+1f0UuwlhxQDewF6H0JP6Q4BoAWNA+izdJJe46x5XCaa\nD4NhW28xWly8gkOLcSH0DoA2o6BfQN9eAdCk3vYh9ARAOxQAugNCn+OVI06NC2j5zs3iSnBo\nMS6EBqDJftc/uwI0cePoOEDvQegJgHZoFEBH65trF0CXJiTrLEaLi5d3aHPOhyYBbdpRvMYG\n9PoSgCb1tg+hJwDaoa4AHSwhc9Eh7R4AACAASURBVIazOS6gk+LlJ2pzLsR+IkC/3Qenp6ma\nyZblyQDdKt1v+xB6AqAdenpAn7MDfJS0ndU32Vs6QFs6PxrQ1Tv5UECfmWmqZpJ+WfXwf6sn\nARy5HxDQb2/7EHoCoB0CoH1GlgZ65+yIPNTchp+ozbkQeyBAa1DYFdDn4QCdRdBSYNLbToSe\nAGiHBgQ05fNZAC3M0+Zcip0f6xbQMhTemgL6HFdP1IQMX5J7AHoTAO0QAC34EAAt9M/7SsHE\nQvaZ0mLnx/oFtEiFGNDO2Aqg4yZk/JLcs6tJ+7NNgB1K7G7VW6AmARcB0A49M6Dz1nIQohnf\nQu0tGiEt5YVMNpSci7HzYx0DWmJCY0Cf/6Qpk1eoJPc7AppoIHa36i1Wk5g3AdAOjQho4rwN\n0HIMqh3fQu0tGZkISlCFTJqSnHPz2DrGR4TRLdoJ0BoQ5rN6BmkzWb8/acaEJJ57AzTVQOxu\n1VuqJlHPALRLALTgg20lBsj75rFMN1AZU5Jzbh5bz/iAMLpFbUiQSeHBW2tAr0fTJnT4otzb\nAX1WTivX9+dGy5LxuRmhAWiHAGjBB9tSDJD3ywMB0JIUHsSAdkc3ZJ4rmuykPfcA9Kp0PzwH\noC9XzX9OxJ93vQag8wZ7AppoLQbI++RBzha8MKYk5/I0soN9A5oDwnpKzSApfpXzNpZicCRf\nihq1NE2gaPZmAdCBLIAO/rjkf84aBtDkYNsScieY8wWAlmZLFVXeQOvNHwjSLRYy7Ukwrkwj\nO9gnoDUiPD+gbRMombxdBKAbERqAduj5AZ1fyTIx+OGy1mKArEseY3spFjLtSTCuTCM7NiSg\n314d0KZ3mKsFQAfSAX0J/+wA0LU0rwN01qAjQOdd8hjba7GQaU+CcWUaynh+7Q1okggxoP3h\nhVXO2pDNipMvRg1bNphBtXRAl/L6OQG93IKeJg7Q/3fVH6f+m/+8JszRzdWYDEBHncWe4BpI\n0Zgwhp5cazFC3oUzwgwljulZJiqgNJ5fjcPNsgD6dkZLIC1hlbM2ZLPi5ItRw5YNZlCt/QAt\n7x+DugT0/L8+rqBdjekITNi72BOZ5gbUX8J5MKqnZINrLkbIe7BGxJm97BW09jv1doZdLFnC\nKsdNmHbFyRejhi1NE3j8HY54PYrveDzlFfRNvQDa1ZgJwcU9U8GFxb7rEEDTIfIevBEAmpBy\n1zM4wS6WLGGVkzZ0u7Lk2x++sAJaaVUnC6ALCQ1AO1QC6LOnMReDDUwFl1b7JhOgqY6iDa65\nGCLvwRsBoAnZAa2jbO4SvxRWOWlDNytLvh3QalpNQSoFQIca6hZHnN1CkQG2JeROEKt906CA\nlrciZ4p3rsyDm1uxAGh78psDWmlUKRrQb3GDstBPC2jlTcKrqgDtqjzvQFkUPvQwgDb+GpAd\nEabDOjQ5V+ZhH/pACdds4fnbzwD0bgKgQxk/SSj9edf+gD4n2S2UC9Dycl+1P6DJu5Jib/6I\nOB/Gosm5Mg/H0MdJAXR04pUBrbSplQnQdQ9GL8l4DkDbtDugs+wWCoA2iDHFO1fm4Rj6OLkA\nbQwZv7QsglQMRbkfDNAMn9+SBlVjLMkAoAX1BOh86bIT3DoTa5wHo8tD8kG3l4MI49rmQ0a3\nOVfm4Rj6OD0I0EoXsRhKct8a0EoTi5RvdJUJDUAXCYAWojH1IfSkm4sxiJPpAXk6dHSTcW0e\nnrGPkvBLdXz++sJ4h6MA0OJfpiW5B6AzLckAoAUdBGgyQL502QlunQFoyzQ8Yx8lBdD8pbUU\nMn5tWgSpGLJMm2pIOR221L1p9i2qAbR/FXItyQCgBRUDuo7QZH82tr7QLQGt1ZMMy/yccECf\nmGlM8zxeFdBxY9MiSNWQZdqYfL3G5pa6N82+RVIOAehIrwhoC9vyE8xCWwDN1Ydgg2wvB8nP\nqUakiVGDBke5OTDDjAjoN+a0K2T02rQIUjVkmTYmX68xmxotYxGg3+LzNeMvyQCgBT0DoM8A\ntHEeI/KZA7SdDTWAls4FmTYVkaHGbDoe0AV/TeZakgFAC3ICmkhvkcgAbHB9pQ8DNLFZ+XFt\nsyFj04dfDtAsuJWY0WtjTfHN8kybishQYzY1WkYhhzyfE0DXEHpJBgAtaARAG1Z6DEDb0EDG\npg+/BKDfmNOekNEB0ypIxZBn2lREhhqzqdUFdBGg3+LzFQaWZADQgp4C0GdijfNgXH0IPckO\nchSxvXE6RGz6MABtDBkdMNYUv1hEpi1FZKmxB6oC0AWrQGhJBgAtCICWepId5DBie+N0iND0\n4ecAdLDP2Us24nRB+LuMNcUvFpFoSxFZauyBkpIIQMcCoKXghrV+IKCVMOK41unkoenDTwDo\neKfLgOa4rY8QHbAtglAMRKItRWSpsQeqDaArCL0kA4AW9AqAtpFVH84ShjiTHDHMJg/NHebm\nwAzUBRgCZcBlkUCd9AwSHrCtglAMVKINRWSpsQeqFNBvZb/I5FqSAUAL8gGaSm+RyAhccMNa\nHwho3is9LcNs8sjcYT7D4wH6utclQHPcNg0SHTGtglAMVKINRWSpsQdKSKLIZwC6Qq8KaPlt\ndDqKYY5UDzkOcSI5YplNFpk+zE+CGagLMASSQRAzgOO2bYzokGkVhGqgEm2oIluRPUwAtF0A\ndBKdHVVdbdaq3kUdjT4vD7sDoM/BUS3HSUfH4JK8u7LoN+kYAhy39bEfA2jhVhfRzWZ9XxUD\numgZCC3JaArok42lxmZrc1drQQ8EdBWhyQBcbNdqU52YKIY5Eh3kOMTx5IhpNmlg+jg7B26c\ngwBddqszYkA5GUhAWzryi0Vm2pB9U5E9SlIWAei0uau1oEEATQdgYjuXm3Oq9TAMx5xWMqQH\nkMajTAVHtRwnHR2DC/JuynpAV5ChH0Cz63mIAGiHOgG0ylwyvwWiAzCxvevNOFU6WIZjTisZ\nio9YZxNF5g9rOU46ukZn5dyU/CZ2gaBXQJNHlX4267vq+QH99+vp9PXv9Pf06fby0+nXcgiA\nNsWRonODGtabcap0MA3HnLaP+xSA9m5Ktn0dn40uegS0yfjOkrJYtwzW6liysRegL6cPfcD5\ny+n3x6vf1x+XQ08KaDq/BaIDMMGNy61dycrtbcMxp+3jPgugPYTmWfoIQFNtAeizCOjKZegE\n0P+cvk3Tt9P36cf1h4+ffmyHAGhTICE8O6phwbNOTBjLJLMe8sDE8eSIZSJZYP6wmuMd9PKA\nZlisZv8Ba2PXboA2V8eSjZ0A/en20+nLx0+Xjx8ul/AQAG0JJERnR7WsOGlVbG4cjjvN9KWm\npU7CGnc6CtBmNgbNAeiogWX4vSWksW4ZzNWxZGMnQJ9mTdP308/p5+mf8BAAbQkkRGdHNS35\nfoAWxyUPx0eUCTjizoe1HLeXmY1B88cCmvr+u/C8MTl8EulEq8nff20cEtJYtQ726liysTug\n/56+Tt9OfwFos8gIXHDbaie9suNia/No0s6zHH4CQMtsZJo/FNDkF5SGDYy54ZPIJFpL/u5r\n45CUxqqFkFYm1pKNXW9x3PT19Pt6XyM4BEBbAgnR2VFta54fFhoLc8y68ONyA5j682EpT+Fh\nLcfNRe1qw7+dJJwqFzuiPD4AvR+ghYVJtWRjJ0B/u74j+O/p88ePPz+umn9Gh54S0Ex+C0RG\nYILb6k0tBaFApEmmXdgBmGGfDtDkruY3pMRSNwckMMRRZb9mQAunqDxryd97bTwS0li1EPzC\nZFqy0RjQ642N2zN1p1/Xo5/uz0JvhwBoSyQhPDtqkegw4djG4Qre46voD0CbuZAElccHoMV/\n+6BmIYSVybRkYydAT7+/nk6ff96Ofj/9e/tzPQRAmyLx4dlRi8SECQZpOlwUvzpA/4DmN6SB\npTXig4oG9gK0WkU7r41HfCKrVkJYmUxLNvBtdoIqAF1BaDICE9tVdnwpSBVyPdtyuCh+dYA8\nQmjVvFptxG1prbkP0O9OLOQxRQMANPFV3MwJ50rwK5NryQYALegQQNMRmNi+umNLQaqQZwR0\nzbCCSOBlG9IH00zv70ZC8yFFv9bkNAc09yvRAeIyaUs8txTC0uRakgVACwKglzEaDhfFrw7Q\nE6BpOGYb0gRTlgXv71ZC6/ZcxEj1HIC2/fbCHTcr6W4wtiRrREB//3I6TZ9/uQMB0FwtSBWy\nF6DPtQEZS9Fh42K1EQnHfENaYCpeQJddQxMnXMRIJSSRTrSe/T0XhxY9dSaTtqSzK0GvDJf6\nJVnjAfrvp9v7kPdn91zaE9Bsgt2iIzCx7aUoiI4Sj9FwuGCA2v5kiPCwdbVaiNmAKf/YDcwG\nC/XuATT1mZTguDS+/q0+FkDTh5V+yrgtxcydzqQx5+xKkAvD/t24JGs8QH89fbs+B3J/yNql\npwF048cqzIBuMlo4QG1//gHB8GfDarUQTUaZlCwgmX3+/l5IaOq4NP4hgN6jyiRxcyczacw4\nuxDkutCpv2pJ1niAXj4s7nxYb3omQLe95QBAt5BIRq5Z3l5s9v5eSGjysDD8+RUAzc7dkljz\nCiyjUOvCpP6qJVkAtCAF0OK9Bu9YRCT6aHjOW5JMLYgVErxsM1wwQG3/jgBNEfBMQIDbv3K4\nlQoGQsdn6GjZUWpCxblg8mzI/k6LQ4qfO5vaeCkszTht4zDulmSNB+j5Fse301dvoMaAPgPQ\ndcPWBmQspa7FHDcTtQHPjQH9/m4gdHqCDpaOQc2nPBl0ng3Z32lxCClz1+T5LYZSMAztb0nW\neICePzJ+uvz2BqoEdLLb40Nsgt2iQ9DxnUXJyAToep4SA1QH6AbQ1AYMj3Pt0vNSs3daeSMf\nIGhKsOSwiMmzIfu7LA4lZe6afDeayAVgh79pSeF4gJ6mfz6dTp++/XUHagro+BCfYLfoEPQA\nvprkNDCgmcMPBzSx/+ITbEN6lwpMkBFtxUY6BjWj8nQweTZkf4/FoeRNPrcWhrbMAvCpv2lJ\nYVNACwnxDhOolw+qkMBMXjaYMB2CTqmQcIeYMOnIADQvYgPGx9l29DYVoSAQ2o4NA6Drb0LT\nh5WuxaN6JE3ekD33m7XiSlBaUghAC+IBnc6r4YzpCPQAQsIdEgEdvm4zXBB/lwChazXHbcRu\nO/61vE2pFgKg35MmJizIlODRYRCTZkv2HwNoKfcGQPN3mApEG1xKFYAWxAI6m1jDGZMRmJwK\nCa9XPtXm8XcJELnWctxE/LbjX8vblGgg8XnmhAcaCqB5dFjEpNmU/QMAbfjbkV8LQ67VpSAM\nLqU6HqD/fg2+1dSlZoDOJ9ZwxmQEJqlCwuuVjQxAM+J3XfLavEuJBgqg371PSe8JaGZX7JP9\nArmTLy2FIdfKSlAGl1IdD9BfTl0BWn4c1y86hFpyO2jvkauDMwEi12qO/bI9EpedYVtSuzQ/\nr/HZDQ3Lr/nFOWLyfFwxx/ImX1wLQ66VlaAMLrU6HqBP8/f/+/V/f5z6b/5znsN6PJpZfiRp\n7RMdQi25HbT3yObgHCqY/pFrNcduWW9Zpqf4lvk2JU77AO2nBjmp4iQxed6hpEpcKrNXc1Wb\nazn1dweF+Pjz53BAfyq+J73PFbT4MIFfdAi15nbQ3gObo3OFzN6a3/MKOjcibLvktXmb5med\nfD4a0EyemxczbZ5pmvbiZq+lqjrXcurvDpZaHe8K+nfJI9A3AdAu7T6wNThXyX0AWtp2yQHz\nNs3PegHtpkY+y+ygQ0yePdm3DM64Z9smvazJ19bCm2sx9bODpVbHA/T079H3oPO5NZwxHUIs\nvZ20+8DOC+guAG3fz9kpZeeLMd18rgf0e37UITrPnuzrYwv+udZ5v7y7lqn6XMu5Px7QIVyX\nnwXidvcmYT43bcYO0SG06ttDuw88IKAd2zk71wbQV/+DANp+mJI2uDwBtrn0ni4dmF+LnQB9\nO7bU6gGAPq3/C34WaNvuTUJvByOgadIUmqRDKNW3i3Yf2A3opJL5D9hEL+Qcu0QYkbZd8TbN\nzoV4vqo9obOJjgZob3N78umlaEhoyuqy0uMB+svhbxLmk1Nm7BEdQi6+fbT7uDsBOr6y1nLs\nUm5E3Hal2zQ7lfL5g9C3/+0F6NuY+WGHmDQ7sq8NLs9Ab27PPr0WuwH6fmxZ6E4ALUE3Pffl\nq/t77O5qBGi5EKgZe0THMI7ZVLuPa4vOV/LDAZ07Ebdd8TbNToWAju7t7UTo+5jpUY+YNNuz\nrw0uT8DS3px9cilaEppyuqxwL4AW7ilntzgOvgctFwI5ZYfoENYxm2rvcf2AjkvZCejqbBJG\nxG1XvE3TMwmfI0Lf/sdCw8GQZKbvHQBaGl2ZgaG5Nfv0Wux2CT0fWha4A0CfTvGxVAA0AE1V\n8qMBTewpedcV79L7623bB4DeSt98JW1kSTLVSkALD5/a+ufLnZ8WZmBpz/SWmzmzahNhdFnZ\ngwF9K7NTeCJXb1+WpBdXNmWH6BDWMZuKG7fiOxri+KZWXCULcRlA828i+I0YAF2+S++v132/\nXj1PAaDtV9JGliRTXRqW5aoRoPnRtRlY2tPd5Ubev/ZsIowuC3s0oMOfxwC0qbySKTtExzAP\n2lLcsA8FNF/KfFwS0OfKbBKbqm5X8tv0/nLd+e/Bu4MLoCuupLXRl1vQrwZo/mMsgbxZtYkw\nuqxoB7c4Jt8tjunvt0P/RRVbfZ2fF9AVv/cm8S2N+FLm43KA9v4OJBnZAdBv0VDh7g/qI7yA\npq6kiwmdTHVpWJSrs/SQuivd8ll+Cqb2ZH+5yd6AXg8tC9oRoI1vEv4+7N8kdD4Z7B2Nis4c\nfoxYQDci9FGALrBKPjVQtSeFjXr/OQX0wuH1upm8km4F6LVhUbLO1YAmXFGn2SmY2pMBxAbe\npFqVG13K9shPEp7Cn81PcXw9ff5A8+/PD/9XvQHou94eCWi+lI1xowxWJLNuA7o26v3HnM/R\nDuGupBl+TOEpfuh1rlu7omydudW1pp+yRZxlp2DrQEUQz/v/3jOPm/hc1nm87+JYyvTxT3E4\nnwz2jhYNlQQRB2p1yyEfmxztbShAxxnUk2n1sZPWsRK6Rg8uBVfU2ZU0i+dbR9sl9Nt+gGbf\n2ODyLZ9lp2BrT0WQzkp8tiFa+dtxO7IsGQAt6NUBTY8WFtTuYktZ0MiAXq/hOEDHxM2vpCU+\nGwm9Dh8d9aoRoMnxheRtbQztqRDSSQXQKqLZJrnRZcXGA/TBtzhM5VU+ZSaIONBLAdowNAXo\n8FUTG7vJBOj5nsU0pVfSN1GAjm6AhOO9h0Ovk83beVO2I6CF3IWNDB2cUgEtI5pvkftcgDAe\noA9+k9BUXuVTpoOI4+yGS/YOx+MAfa9rqpYFjQ3otwCQKaEz9m6FE9+jzlokt6i30d5JQFO0\ncaasCtDysHzqojaGDj4Z+CwwWjqd+1xWcjxAH/eY3RGANvxS/rYXLwVAP4rQ98qmalmQBOiy\nj0fatq+plVE5h5n3AK+n8u/omIKz88kI8OE4WW7faEC3WXM3oPNxhbTFjQwdXNrea03/1Bmt\nADzzuazcgIAuVgtAW6qrZsp0FHGctwfecTgG0E5CE4COXhbaUHevpZVVBIav4i7aggoKQR4e\njO+AhMOkuX1jAN2I0AUJN69G3MbQwSVu01oQ3QWg99GogC4iNB1Eq2WPqzplO+EBwx0OaMvm\n5XZemTL+3jYBh+eQxeGtju3KOgL0NVA4TJLc24mwVXS2WiWAJr9OiFLSxrF+BvG7Vie0CO+3\n5wL0/QuhT58OuQftKsUC0UG0Wva4qlO2Ex4wWs4QWSKgre9S5TZEsZdGZUrByz0/l0E6IXH8\nlMd2NPyWDwLQa7PUlzt1ucoAbf0yo7iNff0smtM55X+SqxF2ldi9Os0Gu2o8QH9bPtlyyFMc\nrlIsEB1FrWWPrSqlO+ERo6Ul7YuRptUPaMPe5XdemdLrYttHBKcc0OEHWZYD0wJoyvV1utuo\nmTFv7oj1WLPqT7m+HEl/6/pZtKaT+JNcoa2rxO7NaDbaVU0BrcyuUAmgL6ef1z9+HfIctK8U\nC0RHUUvZ5atCcUWlJ/cZjrrK8yjN3w6AFi6NylTEZ+rrSElgT3dC07w4h5eKuTNv8vLl2LJa\nkXFOSf/yaPlqBtnMPh5EL1IQSwN09gmZJeZ4gD70gyq+UiwQHUUYJCjEBygsqPzkPsMdDWht\nK4cbUG9rUkBcx3dshI/jZR9guSt4moN3PQVhcm/O7IlpLU85p7R/cbQ8M5MKaIbQxEJRxuPX\nS8jxAP3l9PXv9Vm702dvoAEAzURR6rzRrjFEiSoqO9fERTZaVtLOKHL+Ut/ZANa9zAJafL+I\n7hTz2U7oucMU39pYHq+bIkDzBsJ2xHyc6efTzgfTc84q6V4aLcnNvD15QDOLFIV6EUCvH1T5\n5Q00JqBlwISFWCs9SFxR+ckWLtLhrml5r7mE1lYtjJgP4NjLPGzZ5kynjbc0UUVC30Shgw+X\n7dWHAdr3XRsGpd2rLqDTrLL3oNm/RoN/bkFecvoO9IiAXj6o4v+XY+sB7StBt0EAOou4JKbi\nEtoC6HRjx+fsW5ljLdOa6RWAwQno/F9eWdIXxsuiZXtVAnSjX9ekaIa0c0p7V15AByld8kr8\nGWWbXZPwTO47+DkccEBAFwuAFmUIkm6F9FwDF3HELTPll9A2QGcbhj8Vycha/nYk0SvY2G5A\nRx2TfwprmpjfxfPNunRnU1MrMZwh76zS3m0AHd5pzkX+dRj1z04Ig0ehAWhB/QM6KMtq6VGS\nys9PNnARR7zmZEEKP7SsIj7nl2LB5o1emFD7vvzbVZzoXhN3yasoTBuJCtF0mHUmM/WSwnFL\nYlKLp+qoZEaP04V/ThmgiazP6dxOCqNv7acRAb04v1y8gboFtPKPw1oA3WDX6EHiJaXO1buI\nQl5Tst7eY4dWVAhoTtHuMqNWVdrpOnX3UxwREyaq2+2odo8jADmZgoo1pdJevSSxuared6Up\nk3+PCYqUWq2wiLdV4QeP2w8G6PkNwuQvLKOqAe2UeZwuAK0HSdeUOFntIg45xQ+Glc22LaAj\noFHbNW9sU9QrrRBPoA0L7KmTAuiA41QOahaVSHvtkjRXlkkV0NPG54zQE32FzY4etz8C0KFX\nA2jD898DPn9vaZ1UJaCthA5aMmFKqtwrPUi6psTJahdxxKkFoPVhHIqQRvOPaGxS0C0pEF8c\nXfOWosZeDNxxwwC60Q01NppvSdoryZb6TsC6UFm79Hh4hc2NPh0N6NP6v/hnTswtDr8AaElq\nkGxNqZPVNqKQU1zzDWcbDWNXxDQGf1Rjp6ZpvSYrDyKHn6LgySS3jbkXoMVwriVpLyJd2jsB\ncz6jK2UK3OEVNjf8NDigyzUqoPlf0sMMl5qMQqkNuBEbuUhDTtHeaDfbeBS72sOS2+7UL8t3\nZQ/2FcW/K4gSTvJ28XwYoH1LUijhJnCSKes7AdOU3cpYFfJ5JT03frD6IwJ6nHvQRkCHTZk4\nBVXulRqEWFTibKWLNOI1J+RvhW2HscqNwjJN0i/ViY0SW0lWlzDbLO93N25bj05E47RXLEmp\neD7GeQplXLawy/JyvcERripjIOwHQEsCoJmxsjFbucgGXJKUVnTjYWzygrBUkwDoxEiJsWnK\nL9Djad7fH9zzEloK51mSUqVzTk6teQpkzesU/Jlwygbooz+oEkHZAFry/O/P/9g9zxoW0AVF\n7pUWhFnW/HSdjXzEe9nnFd14GIt8GKzQxAM6sVJkjQwfznN5EK/qEtrzhkbxkhQrnXNyZsmT\n752AbU+ntzRuMbbjRNIjBXQY7wp61t+Tm9B9Ajpq6wqfpLjUZRjLOlYyaJ0L8dO+t/UnrjkK\nxpGGMYjflC48Gne6yGfjJ8iV6Aygt+fwHgZo79dTVSudc3bqveCrqt6zNwvjNM9nJhXQ7wHz\nhgX0EV836pVpkLCtK3qa4lKXUTDjWMmodS4GBvSyiO1AfYtz/R9FhsSNYk4YwgboGRTsssuJ\n9aS9dE1KleczOcOlyZfepP+0lQtv4G2u+VnDAvrf0+M/SeiVaZCwrSt6muJSl1Es21DpsHUu\nxK9juK//bvc4pJnFyrfhlL2LVIHoe285XuJHsqeNlYEnjDSF13xXMcvuXlQ+7UVLUi4yo29x\nFqd6QGdpvmWTubO0aWxAr+8RfmtpndQjAB019gTPUlzqMgpmHCse12ZDuDznR1w/MsFfQlcl\nQJxZqGwTLorfRHFfSd/b07WRNPUYVMfMLtC3QGu6NyfUqi/5c642nfaSJSkXndM8S0WA1j/6\nfdpWl3QXIu/ITxKegp8F0YC+uPn8XIAmclxq86xBTil3G6DZU2SnqFjfJUDXJUCZ2qaMcLOS\nrTgrbiru5VTs21IWh7lVeVgqfHCHY7VDDLdlz7yoQtpLlqRcxLTpLJXwOf/2Oyn7hLvpaEA7\n9dwfVIkaO2ITOS61yT2EwZa3WPzSEOwZ1tH9ak64x1GXAHEm0ZzD3SX8yyWLkitjehdT3zTM\nvy3l96pAJP5Kjq13eAG92MlHkd+3UJaDCudek2JZEvTO/KJhTu66/uzp5NOxq+aPCd0FQAt6\nAKDj1vbQVI5LbXJXoXx5i+UvjMCf4hxtH5lIOJK/PbknoPO9lTxItYKa+ebgZKtOUSAiXg2g\nzQBirg0DQK92xPGYxLrS7lwTZ0aIznJqpvCvT2M+0/7SyQD8mbvBAf3jy8fkvvxbEOjhgDYQ\nOm5sj0zlOD1eFE0Zw7A1hAH4wTlDwWfa3pORCYv2GYtTpOf8nvH5RPzrdMmVNP3L7pQEYt/3\nD2S0GtpVKUISenIDmvkFyJd2x5KUZYXszyRmXptwzZopWHXyAyvzXb1ZowH69+e5Zj4d8E9e\nuaUPETc2B7YVYkk0dQx1Y0gD8OeYDvO1MwXo9N1Jx4S1ORJzvi6WcGuDvZImb33kcY4A9PJ2\nFXF0IcmDAV0yJ7Z9cXqC7WnNpEcT8XtSaG8aGtCfTp9/fPzx8/PpkztQh4BOWpsDC5kOVBJN\nG0PZF9SosiPyzFY322fa+iLtAQAAIABJREFUsoEbPMiiZXCZ87Zi6a0I7hYF146Jk/bLtrXN\n6WrYzIqb4oPhc7uLHWVAOq+VaTfPiGlfmp1pWy1rIj2aCEDn79EuSzMYoL+fPs8/fU6+D/r2\nVPTlciH/1K2TWgBdfndXGyFpbA1rLeuScPIYREWxo9ocUWe24cIPHWvj2icsOcwHoW5tcLcy\n2CvipD1//kS/LSVOm5yDCRWzooPRBysWO/KAdF5dea+bENW+MNa6PNQyNNBEAno1vH4Ryl1N\nAb2Pwm3w+fRz/unniuqbbiC+Qzn/c9bTANpc1yXhxEGycuJHtTqizqzNt/uhjwI0t6fSWxsL\nua6nDG8epv04MM/KHIizNs5CmFZ0cHu4I7QjD0jm1ZP36ukQ7cuCTSxAG2mrEvrsyIAOiji6\nfrlMuwK6mNDKAGlrU0xPZRcEFIeJSkkY1GGIOrUeC+6HEvc4CucrpZLbUeTX32TPO88NpxzA\n7OsUzHFUNdeMrKCILuzXY8m0TtzzYGzmldVwTsb6C0He3h1szsTugBYe31vedZn1HICeYfwC\ngHaWNt1fDCkNFJeS0wvtiDqzHYs+MyF8+IoN78wmu6NSwDIgDSs1ujLmb2nME6PjlaZahUQ6\nrVi3IQNgOC+htcXYYzJBmqS0aQkJFm83QNO3lraT+wHa5Mktwy0OHdD/d9Ufp/6b/xRqTZM8\ngDOYs7C5fSN/N40wVr6sdYaScYhjCaD1S7m6fPKFm93akAo9/ywZe+Vs/Gi4O81UCMIqA+hb\nmrdmJ8PfjOQvQE3qWM9OnCg+b0rffLVcQ3sUki09dR/Xy6pVxwL6X/JNwsu09xX0PpfQ3mC+\nws62iHY0PGnfKTWOziqgt0dyZykjVuVTKFv21oZc7vytD1uc0iTnUyGOTvnfF8HfPxGgfZfQ\n2mrUzcQja5xkldS/hlsoqung6PK2+F2DXUF/cPnz9Ro6esxu5fCOgC4ltBjfGctV1/ke0XZT\ndM6zVUoN6ZNKP3U8eS6h9SVT5xdWoXhrg+5KBfLGKcgwORfq+GYn+zO44t4e61DGzNPaoJDF\ntDoyJzXKVmeWHNdjQxk2OnSKLklGA/S0fFDl8/ZBlctdALS0a7gPRdM9hK1yNZ5Xa4Ehw5zC\ny4kQHZbwhiUj55dWbaNrqlvaSuO4EkzOhjyx2clukYcEMt7jIO6O1RdynsR7/RFVKKVObLJt\nyOj3m8qouoJq2Ca1jLz8PByg5496/0hb7X0FvQehfZEcZS3umng2dAd2ryzWqXr1GbJMKric\nCN+3MUVvAOhpclxTmfekP44xn8JsmDPrvFRAewhNWCss5NhpDhEDqIlkJAmgbkBZ10NuJyuv\nrrDMlh/HAzSjFwa05ZKSPsp+bQ23WTbvXMnqcmxWBtAWQqcDqQmli9Z8TeXZlt4+1nTy82FP\nzKvZCNC2r4NRo2ROgz3DAS1J73aU/dVI+nyofzn0VSQ8JO9ITMHvV8uBpwL0bp8k5ItNlRTf\nFUiqY3XTsJ+KpjuwFXhbD+p3dNEBPbRhs1Jf26ONFgT2ZFTbQv4N2EzmZEYz4iNkA0xTeg/6\n3mU77yE068625oTPYMusQIu5ljecDy8noz+zjbiucjGfybzKCsdNvjBgrw+qyG5KZQO0QU8K\naG3j0J2FoPIF9FZDpqplDNn2avhvL0V7R42eDqRlNCrUoGA7B7QwJT5ANsA80Wn7M74z4AD0\nWzNAk/5SksY3cb37Ow+rv0NgNq2KmE5QbYtBAFpQDOjmhHaFUYpCqhrhWzHo9uQgs2mOWJIB\namTLXo3/cbxw72jhs4GUlPJlehyffZnk50R843CqdNLprVvjB+0tBtVFz00Gy5DdiklvESR/\n0bCKr1iTWw01i+JYYGFaxwI6zEWW4FwAtFjVeuVw18ns92UQx1bT7CWlYIAa2rJXtyu37N01\nJXo6jpJRqkqDCU+dAlqeFR+IGGzJ7fInlRebKdWhDdCxt5RgGdGi8pyyK+z0zxTMS01PylI7\nnctK7HQD6NP6v8lE324AXUZoPrwnil4PprIPZd0qV22moy3hLt5taMteXZ/vWst5HVIOno0j\np5PYMsklmHnTtZOaO3elEBNWRl9eBWmwhJfdmvolI6ckzQHNkC4FNsd321/DxklblzjfVNvF\nz3IKgBbUBNA8oT1BDMVgrJ5Vnuedrna3SxLmuTPP0KbNGgH6PXggVx5MAXTWPirS7BJsOgTP\n7AQrSoWYsTL4/GoKltsQXbFr6pcMnJKUuwROycv8mQPatM72afN946O3UcNqW/+iWDwdDGgL\nfAFoywW0q37m6ZhbXt0mNbSobHzbXs3+SSbjJXQ6jJzLqEizratt2r0k5q20WIg5i6PPr7ZV\nZ42xa1FkL+Uzf6/ZB+YU0OZbG8KS2DLMnniPf29b99Ty89GATvNOqB9AlyGaDe+IYaoDVwG5\nNImPbJYYMO3VHNC2S+hkFCWVUZH2DejKYqHmLI9+ezFN20Z9DKBnF1uVxU9r5M9Fp8Q1gZsu\nYt+KGFPMnljnuU0sPnY0oIOfOfUE6BJEs+HtIYxl8J6ccpYUP8hEAHrbsiU1bNmrUwZo4yV0\nOoycy6hIDwA0jUvjbHzVQk2a8RQ0C1efcVa1AJy5sMru2gzeX8XFGN4CSW/IEX9ORFg9I3Zx\nvanouYvF29H3oNOfCR0P6Hh17FydxUSv32X5Yien/FVFB5+SpzfS1wVVbJhkegv6fX4i1/xM\nrvIcWjZN8hMbeyuxEBxV51JROrqnrdlUAejctd3clFwWUE5vx6cU5IESYEdkdn+lh09cb9N4\ni0cAWhANaDeimeh1O4xZ6/hESVmRsaeYWBO3dRzh9XkSgPY+T2BJbRI9+Z16d2W53o4qc6mq\nH93T2mxK/jq2hGddO6yl47IKlmupxvuf3MZ2f+DeNeVsItxxacDFKm5xCFoBXUdoJnrdBmNX\nWiyNkvJali8g1pTd8vAPqM+TvIIOBrQNoqWWK9NoWvuJclF1g8NYPxZTb8kltONXF8a12jxM\n+mQFdPaUfHyG+tMl14QDcf0tQy5T6gDQ/b9J+GBAm5adX+nwuK+e+CpaTW+vk18qDQMmJ82f\nI8w/VDaVXkJTw0TTXO+gBHOyKU2ZuReR7gcAWjSbtIqyXgNorTFbZWoe3cvlkGu+kbj+hiGX\nVBz5ScJT8LOg4QHNELpsf+1XXHHrZOVOcyKCg/S9AGv8N/UxPwLQ83AOVuipTafpTHA878Ju\naVfDTCSpWdGspq2WkhXscfLY2vbGNuyj7jTx8sw2FdPfMOaSCXwXh6AN0NnFn0t09JLttWN1\nJc2TdcsfeFvPnGyE9rlZKvTeKxg1+6VXjqKnNpmOO8Oxi8JuSVd9JrKMKXa4imrAGD72bWg6\nl9M0pV9+5MxqS7nmmouJoI+6TB2AFvTf+tMO9zgKdteuBRY3z5eNWVEzMH1uwlG1t42kOA/m\n85tzkQgv3Ix2ADTnlm6wvSVgD7/5NrRcy2ldjVPNmjSRMC3b9JkI6rBLCgBoQf8FP5NVtweg\npcVuWWF07OTl1ajwS+ZEAdMUX9GWpug5NHI8O6FZX8o0y5Jc0E8I5yo4Nb+yTeZ02SW03VC4\nutvyH6oGs6KlDrskAIAWFAI6JrQP0CSh/ZurcY3RsaOXV5/pLYxkVY1XtD434S+70YPCmx/r\nFLXMWqbJ51Ubn+7H++bj7QZo7Rm/cLVLLqGtfpJng2ZMm5djD8mT2pHQbwC0STOg77VCLVAN\nof17q3WV0bHDV5P2oNO0AfM6J35sn51pCoiZGKIudYVQWmZN0yzNajz1oCMfhIvtqzeHvcwh\n/7EKx/f2h8atHsJlcP99uYPESYWJLkg5AE2oENBLrdArZFQe3L21KutMLLykfbBqKqDFT83m\n8U3VG40bBaAHEkIpmbVNk8upUVRHNsgBgBaf8YtWu+gutNnAttm8f1/uIcFu+5xnIy913hTQ\n++hgQK+1oi+RoDy4d2dxq3mNFf5JF5pcekmHNe6kbpVsWmSVi4MTytOejJh+gkWIJWd2Ceki\ngmUK+ShFPdNZGFVsMDcZrfZy26F4HuLwc715l2MXSXZ3yHk29rKfAGhBDQGdE9q7yvRaplEp\nUOd99dhbRG2nhA2zod/jWybk4ISItMdjpoaEWHJi1znYgWDwzwxTwTVntZUapFwSa90W0HQt\nHQto0XCjpIuDL5kAoAW1BHRKaO8a00vJWlc+W6XFDkMZbgaueaIaWj4ll2qLl9+heZ8/8WcM\nKic28q9N0+qeG6i075u/3or8MTMkqqIhodNljb78SF2OnSQ63iHn+eBLpgFoQdE96LrPqpxT\nQnvXOF/HJdJyDzi6F7zIUoHE6SyeXM+T65rHULrb+PRHQMJvtVNiinlNc9nAOj9URWd3sZX4\n4+YYLnO6KvUKV/W03a078j1C2XBN0pNGwvBLRQLQgqKnOJJ1c28ZC6BNZXzXGmi5cl3+TECt\nFiF1MowrBQnatwX09kEVxmc6PXlTGAHdwvg+chcbEUIfhZslURX1U4qDz7U8ha/65HM5oIlG\n/PhLCgBoQeFz0OnCubdMQmjfAofrd3OzxlnAuAIyAbVShvS5yQVcd3ulkG++sqSnA27rosSU\nEruGMxg3uN5N7lojIpgG2uaZ/6vn0SrXzykInS/nJJXuvlIMu7JOdcunTxlYEgJAC9oAfWoB\n6IjQvuXdVi8IsfGY+Ed99CdJmfKYB/G9TTNtd4ImacywBCVtj3TRtbxO3wRoNa+9AzqpIkut\nESGcYwY/E1VROaMo9FbSpmLbVWw6TBLSybRhHKysAKAFhYBufQntWdztMiPhMwHmDNQlVToV\nAFq7Zx0d1bft+lV2VClv0zcQenw+p4DOqycvKSKCd8zgRV4VtVMKI2/VYyq2PSWkwyI6e0n/\nbP6EBQDaovXb7BoBOiQ0v7Z8Ec8K7jmftn//MrxwPiX/orynRO8Tpt5H52tKfx46PaxtW+rv\nxCha9heIEpFN7PtggM7Khy4pIoJ3zPBVlPZgZWoTs9SG+vveYyRkw6atNd8/z0DuAYC2aAN0\n83sczMqyaxe4SkicPsWRnp6nYFQ8TtRRqKmoJ7XTtqjqVrgPkN/h0ABdAoo1XP5va6UqiO6T\n7ffjrYaSgkqLigpQ4WddxXV139b0ucImYlfzEAnJMCpozQfIU5B5AKAtigCdEtq8ZtTuygDN\nFe+iax/iypl6si4G9SLb2y5ZMLp6pe7ktdDmiwiXD/FYQCcX0OT8CoK7JAKULqFcfEXxRSY5\nCl/G5dEsN+xqsir+ygNDaCEXVjEfXZU2O2HiDEBbtH1hf35HtPISOltWsnRXXbsQV87hLYzZ\n6KbkynprSet2NmnPVa8QI9tqgR2C0PQWoRNOEJr7G8Sm1V4KaNbYXpIBSlYQJa6k+CoTHUUH\ngtV0fNBeEVs1rN746nMpnpY8jZKdTi4Avd0JYwC0SQGgiQu6kkVbQ0sLRqzaRF0503ftFsOL\n0itpWnl7rqIJd5TN5IlW6xacw5Nvy9IfmWAcWkReEpJzdIc2aFt4qQ6i8+c6QHsInTUPVtnx\nQXtFcdlYP8iptqI7spa1WZTs9Dh9/Jl0Pkv7ZUkBaEExoFNCFy3aElpaL6IEJ/rKedK/I0Pj\nefpwCAdS2R9hMzQhxE11j079hfiWXEJn8+d3GCPy+S5yOHdog/Q9TTUUC1bDg9dddCTIfStC\nB4vJVCdRHW90+TGHo45lfos2epQ9aZ3j+awdliUFoAUF/ybh+ntd5botoaXloj80l5F2diZp\nIrhOBp/WsDZAa4Segn9VTo6b6U0AdPa2afzLtm/fzYCmbrykw3kDm2TZ01lDpWIVPnjdRUfC\n1Js/aC8rrUJDbSRW0lNyv6KvRCna53H6hHWObW8dlpQA0IISQDe8hLYtV1i75ivnpHN+Z2QK\n7llPWXgGpJLFxG10R2WzHYFbEnsLOh83vZTz7TzD49QlYY2S93R4IC8fVhoenPbiQ/EyR+vo\nmDfxK0oGfLYyciv6qbL1W6dftMv5FaAXIvF5BqBNCgBN/WsSRYt2jygtFvd4nePKOeyegjdT\ncoVruoAWCZ1Gjy78g5RKtslb0Nmw2S/b0pbLWpkep9aiFkvc1Er58CLKSiw1xV50iFhkU+Jj\nEXf5LY+hJ2OUnjOrZG/Ta0nGyrOSkGXJMAAtKAJ0/q9JFC3aPaK6WOFecJAt1dadBXQGcOpO\nCFHBwblsyEkfV7FN3+F4Iwlt+2U7nw8FaKofH7NG0qZWqkeQVn5Od9ExoqoMeU8UNl6rRX8M\nPRtCOtfg/V3rdjZl27IQ6e/my4IC0IJiQC8/VS7iLY6yVulWMH+tXKZtMmuYJVoM0ASk4uaI\nXL4RV9PBeDmgqb8Asv4soOkb9PrnX9Ih3qyA3kvCplaKR5RSfU538cF8df2EDhubvoRDDMS2\nqV1N42a2Zdu9EGcA2qQc0PEv3kWLdosiLlXMH+amsFk309OUfYAlBah0j5isouAMMSZ5yyQc\nX/TM3YJOx9rWSrTK3ZGZYns98PmjHrTiEaVUn9dedJBYXblEcoWNTXy2ANo6KbssG9kiPpg2\n+pIZAFpQ9CbhtL2oWsZbEGmpKIJUfwp2tZ9eMcu3NqQdEJwgRiPjWqfD3oIm8mP6ZVvIStRd\n2jZtVV47srQQTnvx0Xx1lRrJFDY2PV6nxzoG0I7vFHQvRLjUALSgBNBrLdmXkV5a8r2cVQlB\n2gA6e1ovvcLdpmreJMyHOhLbYVzjdPj3CJPB1glNMqG1pDyez7sButElNN1cWkVb3LA1uXq2\n0ouiGafkkXsXC9lO+hkWIlxqAFpQ+EGVqJbMy8gsbbqGRNVJXytXrIkAtOHhEL2guYGSuJMd\n0MK45HwSVETOxYEm7erbIm3LMT0KSkeVEsJrLzqar66rSuInaSzVYAlonJFH1qXQm6XBgj7y\n8MtyAtCCIkCHteRYSHJtkyWMS24dcZH2W6BD0/b3jOHK2b7ziHFI25Pp7xvpFnQ02lT+C8ac\n2prnqLMiKOrkKhyLlCBVcxJX1xA3bG1YPUdCm8q+FlqzJNgEQAtqB+jau9DxCkbivDj5I2Bp\n4bJ65ewpaWogInIwvuQy/WuQGyxdFlcecoOeCZMVUNjNXjgWKUGc9uLjafrefenLFkFePXs6\n28qzFlq77IP6+kpE8QFoQTqgC78xKVzAWOHw2S1cWaYvkUmnKAe0ix5JG5/zmP+ewow2ld0B\nYhx4JkyufnlPY+FYpATJfCj24hNRBtO0q7POl6FHPrsArWU8+xwol9lk+CU2AC0ofpMwrCXf\nYmaLGy5grGnKnoczQufa29JunpDlI9ceGV1aEJ3egs4TFQUruANEdzPOVNyOVilVQZeNUXoB\nxiZke/wyL1vTnkHTMjiXo730/BGLYe7DZTYZf4n7UoD+49R/859ELVHLaab1H3aR5mGEL8Vg\nNPc3tTXKV9W+2NuiMKcCA1Su8kDe0Ym//owzFZeWam2M8Yc6GDWwyliGvGn+oxX0KhIZpPKZ\ndJUXz7gaO8iUs5Ksp+2k8b2sWjUyoL0dmA+qJOUTZNu0tJGStZmIxywsyFkDWBrb5C1rV/Bp\nYq6dwjRn+4Uc7Nbcfo9jjs88/GGQa0G5jUh0nLSrMEfhkt3Npu/+mH/0h1osgtBkRrOO6RV4\nIONq7CF5GfjFMPYR0h4MvwR9qStob4cQ0DNU8ivo6Bkry9rmRb9pKgN0EMECKYvcZe0JPk3M\nHZwt99Qbsexo4lYn4z8E0PxGpLevGNhVuWR/o+vZnhHQ8SImy8NUSGCUWyjjYuwhcRXE1bB1\n4dMejr+0BqAFxYB+D78xKSG0a3GFFZqYz0iLikPo7U1y17Un+EQQ8pboadq2fJ5SfrR1ydRx\nZ+0GaNu3fDLbl4/qLV0ygsX1ao/7d43jbKZ/zaZtyArZVrnh43W+x9ClQBZZs050YbMejb+0\nBqAFLYAOSou8hHYurrRCU/atRjJyCCt6B4MKCtsRfcoIuSV93fJ5SvnRtu7CkNRXkrhnbFtT\nZZmJXjfzbExv5eahxPCpxVsHpom0iu/5e9XEkkWrTEleAOdxr6QkqQti6cFmPTKwtAagBRGA\nzr90tGR52fWJHlS+iQOOUM56l4KguraeavQp3drbfLfjREbZSW5pI4aaKP5nzY2z9C0ws9B5\ng7s5pre3bqlYUvzM4r0D3UJYRXL58xUj+1lrL0+mfNx6Ppq7LjHrbP6zE7yBpTUALWgF9F6X\n0Fn38F2y+/9VkTYM/fxBtQrfOqrxp+Sj4NO0EHPdulRGuSlOU0DeKbonlWgNnzQ0/43kW2Bm\nofMGsx+qr7dqF1FRjBbvHZgm2SImv4lw5aT0sy0Elc3lhL5shtbqUloXhe/AJD02sDQGoAVR\ngC65hOZWPe8dPmVmE1uS9hDWoNo1iONhktu6xl/jH955DwDNJiwJR5I3iZ82M+UxzUGZlCiL\nSaqrt2pXWQfILd57MC3ytPufQucBbUo/c8awasHLqoX1Zf/MAZp//3hpDEAL2gAdX0JHn3Nj\nayFcBXqVs87v79Z//sdS0K5doweVdoB76CzX2XujVD65MaYM0DcR95w5Mlgn5tzHtPP89GpZ\nOOUWFcVm8Uy/p5jmfUuvubKWZWH4TGY8TxyzLr5Fk9vUP/PItudNBEaWxgC0IBLQsxz3OLga\nyTtHz4nQWhqawGLeN+o2eVOuUfwjr1lOL23Z9wjP7CU00T+IHoHZTgYuB2USo2x2847eog1E\nRbFYnDtwLYg1NBI6Xpe8G5PyPHHMwvgWTVkSIVP+rxVkT3Bul8YAtCAC0NtJ+yU0UyREX+UC\nOm5q4Ypt3xi2ibwFSke+5jEl6JzddzKb3BBbnORb+pawGf8tU+aSUCIxSlBzwim3TAMQFpce\nTIt0Bf1PoW+rrC5C6IxJ53bKuWRSo6MAnXYAoAUFgA6/xyu+xFMLgiuBvKt2AZ22LviiZl1c\npMw0OQXfyBNxaXvN8GZDylkcKL0Sj1+St6jpSUuzkjatIiFKWHPCKb+oMAaHSw+mBbGKTFqJ\nhuwiyBnP0kavi2/JpDZipmzLwrU3zAOANikH9M3PSSQ0VwZsdWxyXEDbpWwa8xh0UdeNOxG3\nNmIjUtKSSHdFROb5L0zb9GaTX0KUsOaEU37RYVSLSw+mBbWMs6SV3pZHXQIi5XIpkAf1JePb\niHlqCWjOxtIYgBYUAvotI4r1Epo+nvebJ8vWODOcKjagawiumqrGnYhbG5EVrpaJEeYAp0jG\nj/2kM1WTUCI2Slx0wim/6DCaw6UL14JYRvnNwnXkbfMYS8+QTqo6rSvGNhLzVAlo+zffTQC0\nqCaAZo6nvdZBWZoxw+liI3oG4GvaOC5pZGIvbamcZYPx8dILczm56UzVJJSIjRIXnXDKLyaM\nYnHpwjXIky5/MnAbuCGg6XtGzgVjG4lpcn8ztzH91AgAtKAI0G8hAO41Zioq+njaZxuUYUiD\nr4/hIlsGSKwzM+THYxxMk/yuXVa3ypTWeNmFuTm1wpQsG8uvtOqEU34xcRgr2zS5ZlTWpyTd\nwiqzgNbLjnNLVKdjwbhGYpoA6Eg9ATp+hNNSVfSJrM80Kb8lMmOVqGSAeEp5lctj8UMvqWbc\nZHWrTWVdO/meszB1YUqWjeVXWnX8mQJxcWgr2zS5VlTWJ+Hvw2Q5vE85iokjm3kXTOIzAG1S\nb4DeQGqpKvpE2mUOa71NWit/eLGYqkaeyCmHo/4RxqLjRaukipypOwmlyqpOOFUgLg5tZp0m\n14jK+pQBOlN6x8lafnLqyFZN1kvOkvfftrHlnh4BgBYUA3oj9E1CXdHlEpzLjk7K98c0/35c\nZ3i5mioGlqF5Dy8BmokXLpJxrGSq7iQUiq484ZRTbCB+JbcukdGgRZ7t5L3YVNxbwUr5acmj\nmjVZLzFJAHSsvgAd/xMeal1xpZdoqvmCrzK5wivlVDquBs17rf4Rv16GCXBdJM9Q2UzdSShS\nq9rm5fpqzHWeeRMZ0Mkn6jdQJ/eer9KWwJ5xrln1colJqga0gdBrUwBaUALo6DOu8/NwWl1x\npZdoejygPdLKyRXMDs25VosAbRc3VW8SStSqtAUpX41JrGRgLHQaZCVN4RpyLeLknrP8pUrF\ndVdPYkZijhzLxrR2GACgBfGAfl8/3SpXlgSqiDKTWMPWMHtJK6ektRLNDM25ViNANyc0O1Vf\nCorUqrJF8aPQKxk6i6wGacmyOLdfAJ3+Kb4lUFx2uwFazhEAHatPQE/JObq4JE5FjLmGYmvY\nGGU/qfUUt1bjGak5l+of5St0jSQWh2Kmap1/mZpUdY3IlQydRV6DlJCZnCRA32RaAUfZEc98\nNpGWK1+CTXnnHADQglJAk9/jJVWXSqot7BJuqVi1eh8ovZ7i1npEEzWXUt0V0O6ptlN1Qdcr\nN8UAenshpHzKvvpKufdMrYBzLfa9w8GkypVgU9pZBwC0oAzQ1L97KRWYTqo16H0kpWQPkl5P\nSWs9pIWaS6Vea5QeyhTMMJJnqs3UpqgrlbmKAT2FZpcGbMqvjZI3C8V7z+QKONcCgE4EQAel\nqBDapjliUMaVAVvLUtJxc0tUHZtLpcaAbkvokrk2UquyrlNmiwR0+ELIeBA3forDsQLetWi0\nZOoHOLXzbHpNWU/drAKgBeWADh61C566sPCI1RJwA3RVuAbyfqHBVXFr0zDqpl1KdUdA53N/\nnFqVdaVSWzWAzv+N3rs8K8Athenzd+XSAaydZ3qZkp65WQVAC3oEoNeADkD7Hmtz60GAFrC6\nDXtN/61GqaEsoWRlU3+cWlV1tURz0ev7z6aEX5uHf1oXgF+LfQE96QDWzjO9zDlP7MwCoAUR\ngN6+Fzp6btlGJJ4sk+cOh/O5Y7f8X2iQfVWbcSRx266Vuh+giak/TK2qul6Sufjl/VVNxrUF\n4JfA9hUWpZr2ArQ55amdWQC0IB7Q2XPLRiJxYPFdQBu/y6fQU9rTVuFxa+tY0rZdK/Veo/K8\nGuHBNtcmalXVDSSMqu+5AAAcjUlEQVR5i14H+S9KuL4A/ArsCugoDWqWdsg45ecmAFoQBej4\nn1aZqm4cr4XqvIB2fJVPgaukm7HE4+bmwYR9uxbqUwK6TUk3kmAueh3kvyjhFQtAuGyoKAtq\nktonnPRzEwAtSAB0/KVJdLHZ6dQA0MJqO10lXYwlnrS2D8ft261QLYC2A2NrTU/drTJw1Jdz\nQwnmopdB/p0o5pfCuACUzXaK0qBmqX3CaT9XAdCCSEDH/8B3zcNxcRxrmPsK+tDicZX0MNd4\n3NwxILNxtzqda1SZTTEUsrk79QSATqeQnEnbefLtWgolX0WJ/qM3ST7YriapfcIZQxMALUoG\n9FXRvzjvgNIWZx3MRBDm2zDVCnTYSjoYyjvsUTCg4OOemYaANs3dqSJwVBXyDmLdZa/OrQDt\nS39uMm3AHG8P6Pb5ZvxcBUALWgCdICEm9Cw3oZP+TkB7b0LYfcUdLLGDDgXjST7umVlqVAle\nz+ciQE9GQJd+Fu1BSucUnMharem25r0Nn+VEc99r9Edfnnh6aoqap5s3BECLWgEdI4EEtJfQ\nQX/Pm43rGnqxYjYWtzfF3noUjCfYmDObAbr0LrRx6j5NNkDHEyis4D2Vmt2O5428ibeshZ4+\nMdHc2YaA1q6wS7MtGAKgRW2AZgl9M7gB1syfuHtAaCtD3FgJmtsHMMZeOhDDlSqoUyOgt2s6\n6dkQ09w9ip0JjUYFNNGKSHwln70JtC7DZAB0Mj01Ra2zLToCoAUFgD7TBXnzFwDWxJ636I3G\n5Iv6zQhxYyVoaxnBFXvuQNkrVFCma406opfwufQOh/1N+exAT8rt3g8TjdRk+/hsTbOQaO5s\n+l2I0upMBwBa+SAnAC0qBDRN6CkFrAEDYn8/oJXqo2UZwR27JaDDMiUA7f++POugXqXG2DZh\nw7L63VmU3yklBJ39Gj7bszxpgCY/ceMC9CSuTcvV20LJjgBoQRGgSUJPRYDeKtXZP1rFCqrw\ngIubOGOaRrDpGmFZhq1GXdEfwmfDu1fhFos69aZkTrP+UI3EXLv47AM0l2ju7JR91ZYQ+x5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6KD4D0MfqleyrxQxAOwVACzICOjkQktgK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\nrkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Runtime: ~3 seconds.\n",
    "set.seed(224)\n",
    "data_combined_py_valid <- forecastML::calculate_intervals(data_combined_py, data_residuals_valid, \n",
    "                                                          levels = c(.50, .80, .95), times = 100L)\n",
    "\n",
    "plot(data_combined_py_valid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `Python` prediction intervals - residuals from final model fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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O5OAPSGKl++A6CbaDtAhzwB0AD0UgHQ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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Runtime: ~15 seconds.\n",
    "set.seed(224)\n",
    "data_combined_py_fit <- forecastML::calculate_intervals(data_combined_py, data_residuals_fit, \n",
    "                                                        levels = c(.50, .80, .95), times = 100L)\n",
    "\n",
    "plot(data_combined_py_fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `R` prediction intervals - residuals from external validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GsROhi+I/yxAOhmKrXhyvFV7UUv4azuBXTVZKR2wpUCQE8ANKWzAB2MzxH+WAB0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\ngiCoUwHQEARBnQqAhiAI6lT/DyAGs5QpTQi+AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Runtime: ~3 seconds.\n",
    "set.seed(224)\n",
    "data_combined_r_valid <- forecastML::calculate_intervals(data_combined_r, data_residuals_valid, \n",
    "                                                         levels = c(.50, .80, .95), times = 100L)\n",
    "\n",
    "plot(data_combined_r_valid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### `R` prediction intervals - residuals from final model fit\n",
    "\n",
    "* Remember that we didn't fix our hyperparameters in the final model fit so our prediction intervals are, well, optimistic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lO7AFPc/WstbWUDp/xfu+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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Runtime: ~15 seconds.\n",
    "set.seed(224)\n",
    "data_combined_r_fit <- forecastML::calculate_intervals(data_combined_r, data_residuals_fit, \n",
    "                                                        levels = c(.50, .80, .95), times = 100L)\n",
    "\n",
    "plot(data_combined_r_fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### `forecastML::plot()` the final ensemble forecast of `Python` and `R` models\n",
    "\n",
    "* Our final model will be the ensemble of the `Python` and `R` models.\n",
    "  \n",
    "  \n",
    "* When calculating the prediction intervals for this ensemble, the sampling will occur i.i.d. across all `Python` and `R` residuals in--in this case--our 1 external validation window. For extra precision with these uncertainty intervals, one could always go back with fixed hyperparameters and re-train/predict on a number of heldout windows to amass a custom collection of residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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T+/oMW97pzj/QxBtxd0MvNNgKAFIOgh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\noEDQAAAwKP8P3c/Jw9w1Cb4AAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Runtime: ~10 seconds.\n",
    "set.seed(224)\n",
    "data_combined_ensemble <- forecastML::calculate_intervals(data_combined, data_residuals_valid, \n",
    "                                                          levels = c(.50, .80, .95), times = 300L)\n",
    "\n",
    "plot(data_combined_ensemble)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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z0dUq4UXoygxxgQ9HZBIkkgaAczcmhDC/qpbu4jfOjuUXl9frj5fFk/c5QSQfD5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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 720
      },
      "text/plain": {
       "height": 360,
       "width": 720
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "remove_dates <- -(1:(nrow(data) - records_per_day * 10))\n",
    "\n",
    "data_actual <- data[remove_dates, ]\n",
    "\n",
    "p <- plot(data_combined_ensemble, data_actual = data_actual, actual_indices = data_actual$Time)\n",
    "p <- p + theme_bw() + theme(\n",
    "    plot.title = element_text(size = 16, face = \"bold\"),\n",
    "    axis.title = element_text(size = 14, face = \"bold\"),\n",
    "    axis.text = element_text(size = 12),\n",
    "    legend.text = element_text(size = 12),\n",
    "    legend.position = \"bottom\"\n",
    "  )\n",
    "p <- p + xlab(\"Date\") + ylab(\"Electricity demand (MW)\") + labs(color = NULL) + \n",
    "    ggtitle(\"3-Day-Ahead Forecasted Half-Hourly Electricity Demand in Victoria, Australia\")\n",
    "p\n",
    "\n",
    "ggsave(file = \"electricity_demand_final_plot.png\", width = 9, height = 6)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}