ARIMA_Approach_to_Index_2k18_Stocks.ipynb

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    "colab": {
      "name": "ARIMA Approach to Index 2k18 Stocks.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOPEHXEUoHhaXDWGs5qQXU/",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/DataMinati/TSA-Fauj/blob/main/ARIMA_Approach_to_Index_2k18_Stocks.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZRLeWWpij1nI"
      },
      "source": [
        "### 1. Importing the necessary packages"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AoUNIabKjuzF",
        "outputId": "c3249d16-8242-42c9-8d7b-32ed3f4c4297"
      },
      "source": [
        "## Base packages\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from math import sqrt\n",
        "import seaborn as sns\n",
        "sns.set()\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "## For statistical modelling and ARIMA\n",
        "import statsmodels.graphics.tsaplots as sgt\n",
        "import statsmodels.tsa.stattools as sts\n",
        "from statsmodels.tsa.arima_model import ARIMA\n",
        "from scipy.stats.distributions import chi2 \n",
        "\n",
        "print(\"All the necessary packages have imported successfully!\")"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "All the necessary packages have imported successfully!\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GzMbpKGxkMti"
      },
      "source": [
        "### 2. Importing the Dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 356
        },
        "id": "yTmRTXTUkIF6",
        "outputId": "4df80f86-ba19-4c62-9cef-fa2c92b1d1bf"
      },
      "source": [
        "raw_csv_data = pd.read_csv(\"https://raw.githubusercontent.com/MainakRepositor/Datasets-/master/Index2018.csv\") \n",
        "df_comp=raw_csv_data.copy()\n",
        "df_comp.head(10)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>date</th>\n",
              "      <th>spx</th>\n",
              "      <th>dax</th>\n",
              "      <th>ftse</th>\n",
              "      <th>nikkei</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>07/01/1994</td>\n",
              "      <td>469.90</td>\n",
              "      <td>2224.95</td>\n",
              "      <td>3445.98</td>\n",
              "      <td>18124.01</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>10/01/1994</td>\n",
              "      <td>475.27</td>\n",
              "      <td>2225.00</td>\n",
              "      <td>3440.58</td>\n",
              "      <td>18443.44</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>11/01/1994</td>\n",
              "      <td>474.13</td>\n",
              "      <td>2228.10</td>\n",
              "      <td>3413.77</td>\n",
              "      <td>18485.25</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>12/01/1994</td>\n",
              "      <td>474.17</td>\n",
              "      <td>2182.06</td>\n",
              "      <td>3372.02</td>\n",
              "      <td>18793.88</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>13/01/1994</td>\n",
              "      <td>472.47</td>\n",
              "      <td>2142.37</td>\n",
              "      <td>3360.01</td>\n",
              "      <td>18577.26</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>14/01/1994</td>\n",
              "      <td>474.91</td>\n",
              "      <td>2151.05</td>\n",
              "      <td>3400.56</td>\n",
              "      <td>18973.70</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>17/01/1994</td>\n",
              "      <td>473.30</td>\n",
              "      <td>2115.56</td>\n",
              "      <td>3407.83</td>\n",
              "      <td>18725.37</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>18/01/1994</td>\n",
              "      <td>474.25</td>\n",
              "      <td>2130.35</td>\n",
              "      <td>3437.01</td>\n",
              "      <td>18514.55</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>19/01/1994</td>\n",
              "      <td>474.30</td>\n",
              "      <td>2132.52</td>\n",
              "      <td>3475.15</td>\n",
              "      <td>19039.40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>20/01/1994</td>\n",
              "      <td>474.98</td>\n",
              "      <td>2098.36</td>\n",
              "      <td>3469.99</td>\n",
              "      <td>19183.92</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         date     spx      dax     ftse    nikkei\n",
              "0  07/01/1994  469.90  2224.95  3445.98  18124.01\n",
              "1  10/01/1994  475.27  2225.00  3440.58  18443.44\n",
              "2  11/01/1994  474.13  2228.10  3413.77  18485.25\n",
              "3  12/01/1994  474.17  2182.06  3372.02  18793.88\n",
              "4  13/01/1994  472.47  2142.37  3360.01  18577.26\n",
              "5  14/01/1994  474.91  2151.05  3400.56  18973.70\n",
              "6  17/01/1994  473.30  2115.56  3407.83  18725.37\n",
              "7  18/01/1994  474.25  2130.35  3437.01  18514.55\n",
              "8  19/01/1994  474.30  2132.52  3475.15  19039.40\n",
              "9  20/01/1994  474.98  2098.36  3469.99  19183.92"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bU-P92LlkcMr"
      },
      "source": [
        "### 3. Preprocessing the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CkM5tKhgkUfu"
      },
      "source": [
        "df_comp.date = pd.to_datetime(df_comp.date, dayfirst = True)\n",
        "df_comp.set_index(\"date\", inplace=True)\n",
        "df_comp=df_comp.asfreq('b')\n",
        "df_comp=df_comp.fillna(method='ffill')"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lpev3q0oke4Y"
      },
      "source": [
        "df_comp['market_value']=df_comp.ftse\n",
        "size = int(len(df_comp)*0.8)\n",
        "df, df_test = df_comp.iloc[:size], df_comp.iloc[size:]"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dPTsQEwVko1v"
      },
      "source": [
        "### 4. The LLR Test"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uEX-PW-0kjkL"
      },
      "source": [
        "def LLR_test(mod_1, mod_2, DF = 1):\n",
        "    L1 = mod_1.fit().llf\n",
        "    L2 = mod_2.fit().llf\n",
        "    LR = (2*(L2-L1))    \n",
        "    p = chi2.sf(LR, DF).round(3)\n",
        "    return p"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gQT1sVW1kwHW"
      },
      "source": [
        "### 5. Creating Returns"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "enb1IzF2ktTD"
      },
      "source": [
        "df['returns'] = df.market_value.pct_change(1)*100"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zyqSO2ask2vR"
      },
      "source": [
        "### 6. ARIMA(1,1,1)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 337
        },
        "id": "a57-uYRIkzqE",
        "outputId": "dddc0124-62e5-4e28-9892-e1c2840f73e1"
      },
      "source": [
        "model_ar_1_i_1_ma_1 = ARIMA(df.market_value, order=(1,1,1))\n",
        "results_ar_1_i_1_ma_1 = model_ar_1_i_1_ma_1.fit()\n",
        "results_ar_1_i_1_ma_1.summary()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARIMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>  <td>D.market_value</td>  <th>  No. Observations:  </th>    <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>          <td>ARIMA(1, 1, 1)</td>  <th>  Log Likelihood     </th> <td>-27603.666</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>59.134</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Mon, 16 Aug 2021</td> <th>  AIC                </th>  <td>55215.333</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>06:08:44</td>     <th>  BIC                </th>  <td>55241.418</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th>  <td>55224.473</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</td>   <th>                     </th>      <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "            <td></td>              <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>                <td>    0.5656</td> <td>    0.682</td> <td>    0.829</td> <td> 0.407</td> <td>   -0.772</td> <td>    1.903</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.D.market_value</th> <td>    0.7475</td> <td>    0.070</td> <td>   10.652</td> <td> 0.000</td> <td>    0.610</td> <td>    0.885</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.D.market_value</th> <td>   -0.7936</td> <td>    0.064</td> <td>  -12.378</td> <td> 0.000</td> <td>   -0.919</td> <td>   -0.668</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.3378</td> <td>          +0.0000j</td> <td>           1.3378</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.2601</td> <td>          +0.0000j</td> <td>           1.2601</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                             ARIMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:         D.market_value   No. Observations:                 5020\n",
              "Model:                 ARIMA(1, 1, 1)   Log Likelihood              -27603.666\n",
              "Method:                       css-mle   S.D. of innovations             59.134\n",
              "Date:                Mon, 16 Aug 2021   AIC                          55215.333\n",
              "Time:                        06:08:44   BIC                          55241.418\n",
              "Sample:                    01-10-1994   HQIC                         55224.473\n",
              "                         - 04-05-2013                                         \n",
              "========================================================================================\n",
              "                           coef    std err          z      P>|z|      [0.025      0.975]\n",
              "----------------------------------------------------------------------------------------\n",
              "const                    0.5656      0.682      0.829      0.407      -0.772       1.903\n",
              "ar.L1.D.market_value     0.7475      0.070     10.652      0.000       0.610       0.885\n",
              "ma.L1.D.market_value    -0.7936      0.064    -12.378      0.000      -0.919      -0.668\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.3378           +0.0000j            1.3378            0.0000\n",
              "MA.1            1.2601           +0.0000j            1.2601            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ETGVnl1Yk_AJ"
      },
      "source": [
        "### 7. Residuals of the ARIMA(1,1,1)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "id": "zNw191Vdk5V9",
        "outputId": "de00548c-6a6f-412e-c5ec-11f2391f395b"
      },
      "source": [
        "df['res_ar_1_i_1_ma_1'] = results_ar_1_i_1_ma_1.resid\n",
        "sgt.plot_acf(df.res_ar_1_i_1_ma_1, zero = False, lags = 40)\n",
        "plt.title(\"ACF Of Residuals for ARIMA(1,1,1)\",size=20)\n",
        "plt.show()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "id": "eJj_VwSIlB2i",
        "outputId": "33bd062c-64a4-4f12-c6a8-df9f03382211"
      },
      "source": [
        "df['res_ar_1_i_1_ma_1'] = results_ar_1_i_1_ma_1.resid.iloc[:]\n",
        "sgt.plot_acf(df.res_ar_1_i_1_ma_1[1:], zero = False, lags = 40)\n",
        "plt.title(\"ACF Of Residuals for ARIMA(1,1,1)\",size=20)\n",
        "plt.show()"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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rK7O5nqlTp9KyZUs+++wzPvnkEz7++GNUKhX9+/fn+eefp2fPnnWKs7CwkBYtWlhtUNVqtaY2khvV9srYWAK/8XdkrNL95ZdfOHLkiNXP9eSTTzJ9+nTTVerKlSv55JNPePrpp3n//fdr3e4XGxvLG2+8QVJSEmFhYSiKYtZGZo1er2fNmjWo1WpiY2PNphmr1bZv327WFgKYGptLS0ud0vDcGBh7etrzeRt9ssjNzTX1ePr73//O3//+d6vzJSYmmpKFsQ51//796PX6Wrdb1Fbfvn1Zu3Yte/bs4ZlnnqlxXmMPoltvvdXpcWg0Gjp16sSSJUvIyMjgyy+/JCoqij//+c/A743ms2fPtjrWwxpfX1+mT5/O9OnTycrK4ocffmDdunVs2LCBjIwMPvvss2qXNW7P2gkQqLZfu0qlory83Oo0a/3Nk5KSOH/+vOkEV9XBgwdZtWpVtTHeaMyYMYwZM4aCggIOHjzIli1bWLNmDY888ghff/11nUoZAQEBXLlyhfLycotScUVFBXl5eVbrma317LPlxIkTHD58GID4+Phq50tMTKwxCarVanQ6HS+99BIXL14kNTWVTz/91O7j50bBwcGmLrL+/v7ccsstdOvWrcZltm/fbioZDh48uNr51qxZw1/+8hfTa+NFSn5+fpMpXRgvCO0piTb6Not169ZRXl5O9+7dGTdunNV/wcHB7Nmzh/T0dKCyOqNz585kZ2fb7FJoMBiqPRHV1vDhwwkMDOTw4cM1XrF/9913HD58mKCgIJt1tHWhVquZPXs2UNlLSK/XA5gaeH/88cdarVen0zF69GhWrlxJx44dOXDgQI3F3fDwcJo1a8bx48dNpYyqqus73qJFC3Jycqx+T0ePHrV477fffgNg6NChFtN++OGHauOrSWBgIH/60594+eWXiYuLIz8/v9brMoqMjMRgMFjd/z/88AN6vZ6bb765TtswMpYqBgwYUO3vyNfXl5SUFK5evWrXOmfNmoW3tzcrVqwwdf2ujfHjx1NWVkZubq5dDdvGdpwhQ4ZY/RzGktOXX35J1adKG8dNGKtVm4KzZ88SFBRkV/tpo08WxoPcWIVi7V98fDyKoph6Z6jVahYsWIBWq+Xll1/mq6++wtqjyE+dOsVDDz3k9Ooqf39/08jyGTNmmHphVPXTTz+ZurO98MILDvehdlTv3r0ZMmQIZ86cYf369UBlo3K/fv3YsmWLad/d6NdffzWVBHJzc/n1118t5ikuLqa4uBitVltju5GXlxejRo3i6tWrFm0kR44cITk52epyPXv2pKKiwiLxr127lp9++slifuPtJ25MPseOHePdd9+tNr4b7d271+pxY2zLqWtVxr333gvAkiVLKCkpMb1fUlJi6jJrq+u3Pa5du0ZycjIajYbXX3+92t/R0KFDKS4uZuPGjXatNywsjAkTJpCfn2/3KGFrbrvtNt5++21WrFhh0dHiRllZWezatYsWLVqwdOlSq59j0aJF9O3bl/T0dLOxP8a2oUOHDtU61hsZx0U5Ms6lOsYxQ866N1p6ejqXL19m4MCBdpVGG3U11L59+0hLS6Nbt2413t9k3LhxvPPOO6xZs4bp06ej1WoZMGAAy5Yt4/nnn+f555/n7bffZuDAgbRs2ZKioiKOHj3Kzz//TLNmzeql/nLcuHEUFhbyr3/9i/vvv58BAwbQvXt3VCoVv/zyC/v27UOtVvPiiy9ajN6uL0899RQ7duxgxYoVjBo1Cm9vb5YsWcKDDz7I7Nmz+eSTT+jduzcBAQFkZ2dz8uRJTp48SUJCAiEhIVy4cIExY8bQrVs3IiIi0Ol0FBUVsWPHDi5dusSUKVNsJr1nnnmG77//no8//pijR4+axlls2rSJwYMHs23bNotlpkyZwtq1a5k3bx7ff/89Op2O48ePc+jQIVODe1WxsbGsXLmSV155hX379tGxY0d+++03duzYQUxMjN03kHvyySfx8/OjT58+tGvXDkVR+PHHHzly5Ajdu3e3q2t0TUaNGsW3337L119/zT333EN0dLRpnMX58+e5++67GT16dJ22AZW3XSkoKGDIkCE1DkAdP348GzZsICEhwWa7gdHjjz/Ol19+yUcffcTkyZNrVS2nUqlMVaO2fPnll+j1ekaPHl1jI/j48eM5cOAACQkJpvE7t912G4GBgezevdtq9fDp06d5//33zd4rKCgw3aMK4Pnnnzf7jMaBkzdWdefm5vLaa6+ZXhtL3LNnzzaduB999FGzuxxUty7ALAZjyej111839aIbN24c/fr1M1vGWKthrYRtTaNOFvaO5Gzfvj133HEH3333Hdu3bzd1C4yKimLLli2mGwmmpqZSVFRE8+bNCQ8P56mnniI+Pr5WPUvsMXXqVAYPHsyqVavYu3evaZRs27ZtiY+P54EHHmjQW2LcfPPNxMTEsHnzZhISEpgyZQpt27ZlzZo1fPrpp2zevJnk5GT0ej2tWrWia9euTJ482VSHbBwrsH//fvbt20deXh5BQUF07tyZGTNm2LwqhMo66s8//5w33niD7du3c/ToUTp37sy8efNo166d1WTRtWtXPvzwQ/7973+zfft2NBoN/fr144svvmDLli0WySI0NJTVq1fz+uuvc+DAAXbv3k14eDhz587l9ttvtztZzJgxg927d/PLL7/w3//+Fx8fH8LCwnj22We57777nNL77o033qB///6sWbPG1JGjS5cuPPTQQ2bdnOvC3t+RcSDc0aNHOX78uF33QWvTpg333XcfH374Ie+9957ZSc3ZDAaDqbuxrRLX8OHDWbhwIdu2bSMnJ4eQkBCaNWtGXFwcH3/8MadPn7b47V2+fNmiN15JSYnZe08++aRZsjh58iTNmze3uGVJcXGx1Z59xlI9VPbcqhrDyZMnUavVFjc4BKyua/Pmzaa/BwwYYJEs1q9fT3BwsN3JQqVYK0cLIUQTlJ6ezogRI5g4cSIvvfRSndZVUFDAwIEDmTp1Ks8//3yd1qUoCrfddhu33XYbS5curdO6oLJDQ2xsLH/729/sHgfT6NsshBDCWTp06MADDzxAYmJindsqf/zxR7RaLVOnTq1zXCdPniQ/P980kr2u3nrrLXQ6HQ899JDdy0jJQgghqigqKuKjjz7i9ttv98j7RJWUlLBy5Ur69+/v0MBiSRZCCCFskmooIYQQNkmyEEIIYVOj7jp7o7y8qxgM9tWqhYT4k5NT+1Gl9UXicozE5RiJyzGeHpdaraJly+a2Z8TDkoXBoNidLIzzuyOJyzESl2MkLsdIXJWkGkoIIYRNkiyEEELYJMlCCCGETZIshBBC2ORRDdzuzGBQOHwmh3MXCrkpNIBe4SGo1Y4/pEYIIVxBkkUDMBgUliQc4kxmAWXlery9NISHBTIjvo8kDCFEoyDVUA3g8JkczmQWUFquRwFKy/WcySzg8Bnrjw8VQgh3I8miAZy7UEhZud7svbJyPekXLB8dKoQQ7kiSRQO4KTQAby/zp1t5e2noEBrgooiEEMIxkiwaQK/wEMLDAsFQDoqCz/U2i17h9fMEPiGEcDZJFg1ArVYxI74PZO+AnIM8HttdGreFEI2K9IZqIGq1CtXV83D1PH26tnJ1OEII4RApWQghhLBJkoUQQgibJFkIIYSwSZKFEEIImyRZCCGEsEmShRBCCJskWQghhLBJkoUQQgibJFkIIYSwSZKFEEIIm5yWLM6ePUt8fDzDhg0jPj6etLQ0i3n0ej3z588nOjqamJgYkpKSLOY5c+YMvXv3ZvHixc4KTQghRB05LVnMnTuXSZMmkZqayqRJk5gzZ47FPMnJyZw7d47NmzeTkJDAsmXLOH/+vGm6Xq9n7ty5REdHOyssIYQQTuCUZJGTk8OxY8cYOXIkACNHjuTYsWPk5uaazbdp0ybGjx+PWq0mODiY6OhovvnmG9P09957j7vuuotOnTo5IywhhBBO4pRkkZWVRWhoKBpN5QN+NBoNbdq0ISsry2K+sLAw02udTkd2djYAJ06cYPfu3fy///f/nBGSEEIIJ3KLW5SXl5fzj3/8g0WLFpkSTm2EhPg7NH/r1g37pDpvb61d223ouOwlcTlG4nKMxOWYho7LKclCp9Nx4cIF9Ho9Go0GvV7PxYsX0el0FvNlZmbSq1cv4PeSxqVLlzh37hyPPfYYAAUFBSiKQlFREf/85z/tjiMnpwiDQbFr3tatA7h0qWGfgV1WVgFQ43ZdEZc9JC7HSFyOkbgc46y41GqV3RfZTkkWISEhREZGkpKSQmxsLCkpKURGRhIcHGw23/Dhw0lKSmLo0KHk5+ezdetWVq9eTVhYGPv27TPNt2zZMoqLi5k5c6YzwhNCCFFHTusNNW/ePD799FOGDRvGp59+yvz58wF49NFHOXLkCACxsbG0b9+eoUOHMmHCBJ544gk6dOjgrBCEEELUE6e1WXTp0sXquIn333/f9LdGozElkZpMnz7dWWEJIYRwAhnBLYQQwiZJFkIIIWySZCGEEMImSRZCCCFscotBeUKI+mUwKBw+k0POoUxC/L3pFR6CWq1ydViiEZFkIYSHMxgUliQc4kxmAWXlery9NISHBTIjvo8kDGE3qYYSwsMdPpPDmcwCSsv1KEBpuZ4zmQUcPpPj6tBEIyLJQggPd+5CIWXlerP3ysr1pF9wv9tYCPclyUIID3dTaADeXuY36PT20tAh1D1vkCfckyQLITxcr/AQwsMCwVAOioLP9TaLXuEhrg5NNCKSLITwcGq1ihnxfSB7B5orP/N4bHdp3BYOk95QQjQBarUK1dXzaMuz6dO1lavDEY2QJAsPZ+xff+5CITeFBkj/eiFErUiy8GDSv14I4SzSZuHBmmr/eoNB4dCpy2z47iyHTl22++mJQojqScnCg9XUv95T662lNCVE/ZCShQdriv3rm2ppSoj6JsnCgzXF/vUyWlmI+iHJwoNV7V9PzsEm0b++KZamhGgI0mbh4Yz967l63mPbKaoylqaOn70IKi0+3lqnlKZUtcivtpdp2KStuh6Q6obAavPZ6oO9FzGKYtlhwVYXBiuLmN5ToYCq8rVitjKFktJyKvQGi51kvj77O1BYi6M2rpaUU1ZhML320qpQ1fPxJMniOkX5/YCxOr3aBa2/qSiASnV9fcr1bVROLa3QA9an5ReWUlJWQXUnEnsP0qpTDNcXulpaUWV55ff/2nEAq/KKKSwptz1jHSgWf1Q33+8zKLlXKbhaZjb9kZE388wLieATzJSpU4js2NIUu/Hz2/ubVRSlyj6q/Lvqycr6SUihuEKhoKDE9vot/qg9Wyei0nI9eoPC+ctFZtu0FoNiI6A6nfSs7L/LRWU291dNJ/xah2KxE6pOgxZXK7hypbq4FCt/NYz8kgquXCkGQKNW076NP95aSRb1TgHOXSyiokqmruv6qv4CjX9eK6sA4LesQrOZq/4wW5RUkJ9f7JQ4jK6VVdbhp2fXvt7+apnB6XE5Q0m5YjWu0vw0II3ggEe4kNvwcStqDfkFpQ2+3ZoYr5ALi8psz9zAfMoNXCvV256xgekNSuV+czMGg4Jeb0x0DROfJIvr9HqFcicli+oYU4L0+xdCNDbSwC2EEMImSRZCCCFskmQhhBDCJmmzEEIIBxkMCmeyCriYV0Kbls0I1wU2yPgl43YLTuUQ2ExLuC4QTQONm5JkUYWrDgAhRONhMCgk7jhFVk4x5RUGvLRqdCF+TLira72eL6rb7n1R/1Nv26xKksV1rjoAhBCNy5msAtN5AqC8wkBWTjFnsgro2q5Fg2/3dGYBnetxu0bSZnHd6cwr1R4AQghhdDGvxKKbfXmFgYt5tgdh1s92G2YckSSL67Jzi11yAAghGpc2LZvhpTU/dXpp1bRp2cxF2/Wr1+0aSbK4rm2wn0sOACFE4xKuC0QX4oeiL0dRFFOVdbgu0CXb7RJWv9s1kmRxXZewFi45AITwZAaDwqmMK+w5ms2pjCsecfcCtVrFhLu6UnZ+GxUXDzDqjk4N0rZZdbuGyz812HaNnNbAffbsWWbNmkV+fj5BQUEsXryYTp06mc2j1+t5+eWX2bVrFyqViscee4zx48cDsGLFCjZt2oRarcbLy4tnnnmGQYMGOSs8m/zO0x8AABvPSURBVIxfxMLXFqP2DeHe8ROkN5QQdeDJnUbUahWGwnMYCs/Rtd2jDb/dkgy6tnukwbYLTkwWc+fOZdKkScTGxvLVV18xZ84cVq1aZTZPcnIy586dY/PmzeTn5zNmzBhuv/122rdvT69evXjooYdo1qwZJ06cYPLkyezevRtfX19nhWiTqw4AITyRq3oNifrhlGqonJwcjh07xsiRIwEYOXIkx44dIzc312y+TZs2MX78eNRqNcHBwURHR/PNN98AMGjQIJo1q2wfiIiIQFEU8vPznRGeEMIFXNVrSNQPp5QssrKyCA0NRaOpfEKZRqOhTZs2ZGVlERwcbDZfWFiY6bVOpyM7O9tifevXr+emm26ibdu2DsUREuLv0PytW1c+Pa1CbyCnqPIhJ1pt5WcICnJ+DwN71+3sbTvrM9XHPnEGa3HV5/doL3fbXw29T8LbB7H/+AWzh/R4a9WEtw+yGoO77S+j6uJy1TF243bVKhVBQX40b+ZVv9ut17XXwv79+1m6dCkffPCBw8vm5BTZ3YDWunUAly5VPt9BAQoKSigr11NRUXlP/fp4doM96w4K8nP6tp3xmeojLmeoLq76/B7t4Y77q6JCj1arabC42gT60DbEj98y80CtxdtLQ9sQP9oE+ljE4I77C2qOy1XH2I3fo0atIt9PS3GR4xVFarXK7otsp1RD6XQ6Lly4gF5fufP0ej0XL15Ep9NZzJeZmWl6nZWVZVZ6OHjwIM899xwrVqwgPDzcGaEJIVzEVb2GRP1wSrIICQkhMjKSlJQUAFJSUoiMjDSrggIYPnw4SUlJGAwGcnNz2bp1K8OGDQPg8OHDPPPMM7z11lt0797dGWEJIVzM2Gmk4tJBurZrIYmiEXNaNdS8efOYNWsWb7/9NoGBgSxevBiARx99lKeeeoqePXsSGxvLzz//zNChQwF44okn6NChAwDz58/n2rVrzJkzx7TO1157jYiICGeFKIQQopacliy6dOlCUlKSxfvvv/++6W+NRsP8+fOtLr9mzRpnhSKEW5K7GovGzO0auIXj5CTk/tx5gJocP8IekiwaOXc+CdnSlE5S7jpArTEfP6JhSbJo5Nz1JGRLUztJ1TRAzZXfU2M9fkTDkxsJNnKNdZRsTScpT+Sq21rb0liPH9HwJFk0cu56ErKlqZ2kXHVba1sa6/EjGp4ki0bOXU9CtjS1k5S7DlBrrMePaHiSLBo5dz0J2dIUT1LuOECtsR4/ouFJsvAA7ngSskVOUu7DlceP8eFI235M95iHI3kq6Q0lXEaeH9K0eWqPOE/tEi7JQtSap/4oRMPwxG67npoAQZKFqCVP/lGIhuGuY0/qwhMToJG0WTRxxjrjPUezHaozbmrjJITzeWKPOE/uEi4liyasLqUDT7wqFA3L2COu6sORHOkR547VoMYEWPW30dgToJGULJqwupQOPPGqUDSsqj3iDJd/cqhHnPFCJ3lPGruPZJG8J43EHadc3pvKk7uES7JowupSZPbkH4VoOKYecTk/O9Rt112rQT25S7gkiyasLqUDT/5RCPfnzm0DjXHckz0kWTRhdS0deOqPQrg/qQZteJIsmjApHYjGSqpBG54kiyZOSgeiMZILnYYnyUII0SjJhU7DkmQhhBDCJkkWQgghbJIR3EII4SbccVS6kSQLIYRwA+5+c06phhJCCDfgrqPSjSRZiCantnfaFaI+ufOodJBqKNHEuHtRXzRd7n7HWilZiCbF3Yv6ouly91HpkixEk+LuRX3RdLn7qHRJFqJJkRvQCXfmzqPSJVmIJsXdi/pCuCtJFqJJcfeivhDuymnJ4uzZs8THxzNs2DDi4+NJS0uzmEev1zN//nyio6OJiYkhKSnJrmlCOJM7F/WFcFdO6zo7d+5cJk2aRGxsLF999RVz5sxh1apVZvMkJydz7tw5Nm/eTH5+PmPGjOH222+nffv2NU4TjZM737pACFdprL8Lp5QscnJyOHbsGCNHjgRg5MiRHDt2jNzcXLP5Nm3axPjx41Gr1QQHBxMdHc0333xjc5pofIzjGZL3pLH7SBbJe9JI3HFKBsCJJq0x/y6cUrLIysoiNDQUjUYDgEajoU2bNmRlZREcHGw2X1hYmOm1TqcjOzvb5jR7vfPVUfIKSu2a18tbQ3mZ3vS6pKwCRQHvzvcA8Pm3/+fQtu1hz7q1WjUVN3TtrOu6bW23LnFVt2xJaQU5V65h/AmUVxhIv1DER9+coJmP1uby9nI0Lmdtt77iqk/ene9BpVLV6hipiaIoXCvTU1ZhwFurxtdbg0r1+5WyPd9FdXHZ4qrv0da26/K7cHR/qQAfbw1qleOlk5aBPsx+6Da75vWoEdxaLw1e3hq75zfOqyig1SsoKHT9nz/UuMzpU78C0KVrhEPTAJet29Z26xJXdctWlCjceK2kABUGBW2Vrqs1bdvWZ65NXPZOr8t3UZe46rLu+jxGqlu3oihk55RQUloOqFCrVfh4aWgb4mdKGHX5Llz5m6qP/WnP76I2+0ur1aDROJ4stF72ny+dkix0Oh0XLlxAr9ej0WjQ6/VcvHgRnU5nMV9mZia9evUCzEsTNU2z1yN3R9pdnGvdOoBLlwqByi/rbGYBZeX6mhcC5m9eAsD4h+92aJo95m9eglarqZd110VNcVXnVMYVkvekWdy6IOqWdnRt18Lu7UL1n7k2cdmrLt9zXeKyZ921jQsgKMiP/Pxip8V1KuMKyZfSUKkqT3SKAnqDwq3/09ru77mmuJzxm6pueVccX874XYD5/tKoVXTUBeKtdbxVwZG2Eqe0WYSEhBAZGUlKSgoAKSkpREZGmlVBAQwfPpykpCQMBgO5ubls3bqVYcOG2ZwmXMdgUFAH3IQ6pLdDN90zjmcwDoCT8QyeSUbEO6Yx/y6cVg01b948Zs2axdtvv01gYCCLFy8G4NFHH+Wpp56iZ8+exMbG8vPPPzN06FAAnnjiCTp06ABQ4zThGsbGOO/2UaDWkrwnze6b7hnHMzTGXh/Cfu5+8zt305h/F05LFl26dLE6NuL99983/a3RaJg/f77V5WuaJlzDeNM9lcYLML/pnj1FZrVaRdd2LRwqXovGxXilfONdfBvDlbKrNNbfhUc1cAvnqqmKobEd6KJ+NOYrZeEYSRaiWlLFIOzRWK+UhWPk3lCiWo25MU4I4VxSshDVqlrFUHCtgkBfrVQxCNFESbIQNTJWMdS2f359MXXp9WvFqYwrHpHETJ/JN8RjPpPwHJIsRKNTly697soTP5PwLNJmIRqdql16VSqVWz1Hu7aDGN35MwkBkixEI+Suo4arlg7UrW516I6i7vqZhDCSZCEaHXd9jnZdSgfu+pmEMJJkIRodd+3SW5fSgbt+JiGMpIFbNDru2qW3LoMY6zoSWnpSifomyUI0Su7Ypbeu90mq7Uho6UklGoIkCyGcxFUlnrre8FEIe0iyEMKJXFHikRs+ioYgDdxCNHLSk0o0BEkWQjRy0pNKNASphhKikZNnSoiGIMlCCA8gz5QQ9U2qoYRbMo4b0La+xaF7LAkh6oeULITbkXEDQrgfKVkItyN3YBXC/UiyEG5H7sAqhPuRZCHcjowbEML9SLIQbkfGDQjhfqSBW7gdGTcghPuRZCHckowbEMK9SDWUEEIImyRZCCGEsEmShQNkVLEQoqmSNgs7yahiIURTJiULO8moYiFEUybJwk4yqlgI0ZTVOVmUlJTw9NNPExMTw/Dhw9m+fXu18yYmJhITE0N0dDQLFizAYKg8+W7dupWxY8cycuRI7rnnHj744IO6huV09T2q2Ngeog7pLe0hwq1IW50AJ7RZrFy5En9/f7Zs2UJaWhr3338/mzdvpnnz5mbzpaens3z5ctavX09QUBCPPvooGzZsYMyYMbRu3Zr//Oc/hIaGUlhYyNixY+nVqxf9+vWra3hOYxxVnJVTTHmFwamjiqU9RLgrOTaFUZ1LFl9//TXx8fEAdOrUiR49erBz506L+VJTU4mOjiY4OBi1Ws348ePZtGkTAL179yY0NBSAgIAAunTpQkZGRl1DcyrjqOJRd3Tijz11jLqjk9N+MNIeIuzhiit8OTaFUZ2TRWZmJu3atTO91ul0ZGdnW8yXlZVFWFiY6XVYWBhZWVkW850+fZpDhw5x22231TU0pzOOKr6jR1u6tmvhtCsraQ8RtlS9wte26UvynjQSd5yq94Qhx6YwslkNFRcXR2ZmptVpe/bscWowFy9eZNq0acydO9dU0nBESIi/Q/O3bh0AQIXeQE5RORV6g40laqbVagAICvJzaLnw9kHsP36Bsio/Sm+tmvD2QaZ11XbdzuTKbdekPuKqaX/b+104M64TablkX7/Ch8oTdnZOMRcLSvlDp2CH1uVIXPYcm85Sl31dnbp8j+7wm6uJMS61SkVQkB/Nm3nV6/ZsJot169bVOD0sLIyMjAyCgysP2KysLAYOHGgxn06nM0s6mZmZ6HQ60+ucnBymTp3KI488wogRI+z+AFXl5BTZfaXVunUAly4VAqAABQUllJXra7Vdo4qKyuXz84sdWq5NoA9tb2gPaRviR5tAH9O6artuZwkK8nPZtmtSX3HVtL/t+S6cHdeZ8/lmJ2yAsgoDZ87n0zbI1+71OBqXPcemM1QXV12P+7p8jxUVerRajdsf9xq1inw/LcVFjlcUqdUquy+y69zAPXz4cBISEujZsydpaWkcOXKEJUuWWMw3bNgw7r//fp588kmCgoJISkpi5MiRAOTl5TF16lTuv/9+xo8fX9eQGp2qd1ktuFZBoK9W7rIqzBh741WtEmqIZ3zIHYCFUZ2TxcMPP8ysWbOIiYlBrVazYMEC/P0rM9XSpUtp06YN9913Hx06dGDatGlMmDABgDvvvJPRo0cD8N5775GWlkZCQgIJCQkAPPDAA9x77711Da/RMLaHuOsVvHCt+uyNZ4vcAViAE5KFn58fb731ltVpf/vb38xeT5w4kYkTJ1rMN3PmTGbOnFnXUITwWHKFL1xN7g0lRCMhV/jCleR2H0IIIWySZCGEEMImSRZCCHEDuVebJWmzEEKIKuR+WNZJyUIIIaqQ+2FZJ8lCCCGqkPthWSfJQgghqqjvZ9c0VpIshBCiCuNoeWPCaMjR8u5MGrgbAVPPDN8QTmVckZG7QtQjuVebdZIsrlOpKv85QmmA3nTSM8O9SOJuGuRebZYkWVCZJNqGNLc9oxnLTOHrXbk7O+oCrycSxTSn8bWiGF9X/lH1taJAYKAvWtXv6z6Wlkt2ruVzDC4XXCOyU0uHEpbC9W1aCd/WegL8vFAqfBzbltnrOqhh4ebNtOjLve1bXDH+7/cVVve5NdcTgF8zL1AUDIqCwaDw6eaTZom7Xavm3B/TDdUNVxpajRpvL02NcTnbjfvcGq1GZVEfb74Omxtxot9Xplar0GpUFlON72iqTlOs/mnBYFDQBNyEyjeEM5kFhIcFor7+PSkopnXfeJHYEBeBjZEkCwAFmnnX/YdtvMCs7bpUKmjVyh/vKsniSmEp5eWWPTOuXC2lTVBtG9wcvxJu1cqfy07YR87WqpU/l32Kqp3uaGnRyJj4O7UNML136P8um7pUAqYulUUl5fT5n1bA7yev4JbNycmt34fRGDlycmvZ0o/85l6mOG9MpNWdfqvdRi138I3raxnUjDw/y9ORr8/17+F6e4FiligqT/iWoakw6BXeWvMz3h2iQKUlec9ZOukCmX5v7+slQQUfi4u739ds/I0EBPoS6Kv9fSs3bPDGbVteiNVP5gkIaIa/z+9J/8ZEWx8kWbgR4wFb9cDtEBqAt5eG0ioPZvL20tChTUAdroBqt6DippdcNcVV25CN66w6cjctu8DiAVll5XrOXSikd9dWZu9rNOpapOTaceR87e2lQaVSWcamsvijQTXz9aJIY1niMUbjZWVaTQ6lXSYtqxDUlQm7tNxAWlYhJ9Pz6HP9uzJe3PnWUAJsGeBLxbVyh7bdEFoFNUMpr2jQbUpvKDfXKzyE8LBAfLw0qAAfLw3hYYH0Cg9xdWhNzk3XE3dV3l4aOoQGVLOEcJVzFwqtJvb0C4Uuiqjxk5KFm1OrVcyI78PhMzmkXyikQ2gAvcJDpFHVBYyJ+0xmZQnDWxK327qpuhK5JPZak2TRCKjVKvp0bWUqPgvXkMTdeEhidz5JFkI4QBJ34yCJ3fkkWQghPJIkdueSBm4hhBA2SbIQQghhkyQLIYQQNkmyEEIIYZMkCyGEEDZJshBCCGGTJAshhBA2SbIQQghhkyQLIYQQNkmyEEIIYZMkCyGEWzIYFJTm7VGCe3Po1GWzZ4uIhifJQgjhdgwGhSUJh6DtXRB8C+9+9QtLEg5JwnAhSRZCCLdz+EwOZzILKp90p1JRWq7nTGYBh8/kuDq0JkuShRDC7dT3k+6kistxdU4WJSUlPP3008TExDB8+HC2b99e7byJiYnExMQQHR3NggULMBgMZtNLS0u55557GDt2bF3DEkI0YvX5CFup4qqdOieLlStX4u/vz5YtW3jnnXd46aWXuHr1qsV86enpLF++nISEBDZv3sxvv/3Ghg0bzOb597//Te/evesakhCikavPZ89LFVft1DlZfP3118THxwPQqVMnevTowc6dOy3mS01NJTo6muDgYNRqNePHj2fTpk2m6T/++CNpaWnExsbWNSQh6kSqKFzP+KS7x2O7M2ZQZx6P7c6M+D5OedJdfVdxeao6PykvMzOTdu3amV7rdDqys7Mt5svKyiIsLMz0OiwsjKysLACKi4t55ZVX+M9//kNaWlqtYwkJ8Xdo/tatnfvwdm9vrVPW6+y4nKUpxKU3KMx9b09lFYVKy3sbfiGiY0vmP3YHGgdPVE1hfzmTtbhiQgOdvp2e3drwzb5zXCv7PWH4eGvo0a2N1Rga0/6qTzaTRVxcHJmZmVan7dmzxylBvPbaa0yaNInQ0NA6JYucnCK7rwJbtw7g0iXnXkmUlVUA1Gm99RGXMzSVuA6dusyJtLzKKgrgWpmeE2l5bNuX5tDjOZvK/nKWhoyrY4gfnXWBnMksoKxcj7eXhs66QDqG+FnE4On7S61W2X2RbTNZrFu3rsbpYWFhZGRkEBwcDFSWIAYOHGgxn06nM0s6mZmZ6HQ6AA4cOMDOnTt5++23KS0t5cqVK4waNYrk5GS7PoQQzlJTFYU8y9kzGKu4Dp/JIf1CIR1CA+gVHuKUKi5PVuc2i+HDh5OQkABAWloaR44cYdCgQRbzDRs2jK1bt5Kbm4vBYCApKYkRI0YAkJyczLZt29i2bRtvvPEG3bp1k0QhXKI+e+EI96FWq+jTtRWj7uxMn66tJFHYoc7J4uGHH6agoICYmBgef/xxFixYgL9/ZbFm6dKlfP755wB06NCBadOmMWHCBIYOHUr79u0ZPXp0XTcvhFPVZy8cIRozlaIoHtPVw9VtFg8/PAWAlSs/qfU6PL2O1NnqIy6DQalzFUVT2l/OIHE5xi3bLIRoaoxVFNJGIcTv5HYfQgghbJJkIYQQwiZJFkIIIWySZOEkcosIIYQnk2ThBHIXSyGEp5Nk4QRyF0shhKeTZOEEchdLIYSnk2ThBHKLCCGEp5Nk4QRyiwghhKeTEdxOIHexFEJ4OkkWTiK3iBBCeDKphhJCCGGTJAshhBA2SbIQQghhkyQLIYQQNnlUA7ejvY/ctbeSxOUYicsxEpdjPDkuR9bhUU/KE0IIUT+kGkoIIYRNkiyEEELYJMlCCCGETZIshBBC2CTJQgghhE2SLIQQQtgkyUIIIYRNkiyEEELYJMlCCCGETR51uw97nD17llmzZpGfn09QUBCLFy+mU6dOrg6LqKgovL298fHxAeDZZ59l0KBBDR7H4sWLSU1NJSMjg+TkZLp16wa4fr9VF5er91teXh7PP/88586dw9vbm44dO7JgwQKCg4M5dOgQc+bMobS0lHbt2vGvf/2LkJCGeXpiTXFFRETQrVs31OrKa8XXXnuNiIiIBokLYNq0aZw/fx61Wo2fnx//+Mc/iIyMdPkxVl1crj7GjJYvX86yZctMx3+DH19KEzNlyhRl/fr1iqIoyvr165UpU6a4OKJKQ4YMUX799VdXh6H88MMPSmZmpkU8rt5v1cXl6v2Wl5en7N271/T61VdfVV544QVFr9cr0dHRyg8//KAoiqKsWLFCmTVrlsvjUhRF6datm1JUVNRgsdyooKDA9PeWLVuUMWPGKIri+mOsurhcfYwpiqIcPXpUefjhh02xuOL4alLVUDk5ORw7doyRI0cCMHLkSI4dO0Zubq6LI3Mf/fr1Q6fTmb3nDvvNWlzuICgoiIEDB5pe9+nTh8zMTI4ePYqPjw/9+vUDYOLEiXzzzTcuj8sdBAQEmP4uKipCpVK5xTFmLS53UFZWxoIFC5g3b57pPVccX02qGiorK4vQ0FA0Gg0AGo2GNm3akJWVRXBwsIujqyzeKopC3759+fvf/05gYKCrQwJkv9nLYDDw+eefExUVRVZWFmFhYaZpwcHBGAwGUxWLq+IymjJlCnq9nsGDBzN9+nS8vb0bNKbZs2fz3XffoSgK//u//+s2x9iNcRm58hhbunQpo0ePpn379qb3XHF8NamShTtbvXo1GzZsYM2aNSiKwoIFC1wdUqPgTvvtn//8J35+fkyePNllMVhzY1w7duxg7dq1rF69mlOnTrFixYoGj2nhwoXs2LGDZ555htdee63Bt18da3G58hg7ePAgR48eZdKkSQ22zeo0qWSh0+m4cOECer0eAL1ez8WLF92iesMYg7e3N5MmTeKnn35ycUS/k/1m2+LFi/ntt9948803UavV6HQ6s2qf3Nxc1Gp1g5cqbowLft9n/v7+jB8/3qXH2pgxY9i3bx9t27Z1q2PMGFdeXp5Lj7EffviB06dP8+c//5moqCiys7N5+OGH+e233xr8+GpSySIkJITIyEhSUlIASElJITIy0uVVKcXFxRQWFgKgKAqbNm0iMjLSpTFVJfutZm+88QZHjx5lxYoVpuqcHj16cO3aNX788UcAvvjiC4YPH+7yuK5cucK1a9cAqKioIDU1tUH32dWrV8nKyjK93rZtGy1atHD5MVZdXD4+Pi49xh577DF2797Ntm3b2LZtG23btmXlypU88sgjDX58NbmHH50+fZpZs2ZRUFBAYGAgixcvJjw83KUxpaenM336dPR6PQaDgS5duvDSSy/Rpk2bBo/l5ZdfZvPmzVy+fJmWLVsSFBTExo0bXb7frMX1zjvvuHy//d///R8jR46kU6dO+Pr6AtC+fXtWrFjBTz/9xNy5c826NrZq1cqlcT3yyCPMmTMHlUpFRUUFt9xyCy+++CLNmzdvkLguX77MtGnTKCkpQa1W06JFC2bOnEn37t1deoxVF1dgYKDLj7GqoqKieOedd+jWrVuDH19NLlkIIYRwXJOqhhJCCFE7kiyEEELYJMlCCCGETZIshBBC2CTJQgghhE2SLIQQQtgkyUIIIYRNkiyEEELY9P8BqB89/3IVsrcAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nnCUvUm5lJB3"
      },
      "source": [
        "### 8. Higher-Lag ARIMA Models"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rFOf_QsjlFam"
      },
      "source": [
        "model_ar_1_i_1_ma_2 = ARIMA(df.market_value, order=(1,1,2))\n",
        "results_ar_1_i_1_ma_2 = model_ar_1_i_1_ma_2.fit()\n",
        "model_ar_1_i_1_ma_3 = ARIMA(df.market_value, order=(1,1,3))\n",
        "results_ar_1_i_1_ma_3 = model_ar_1_i_1_ma_3.fit()\n",
        "model_ar_2_i_1_ma_1 = ARIMA(df.market_value, order=(2,1,1))\n",
        "results_ar_2_i_1_ma_1 = model_ar_2_i_1_ma_1.fit()\n",
        "model_ar_3_i_1_ma_1 = ARIMA(df.market_value, order=(3,1,1))\n",
        "results_ar_3_i_1_ma_1 = model_ar_3_i_1_ma_1.fit()\n",
        "model_ar_3_i_1_ma_2 = ARIMA(df.market_value, order=(3,1,2))\n",
        "results_ar_3_i_1_ma_2 = model_ar_3_i_1_ma_2.fit(start_ar_lags=5)"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_EYpc3ZllMlH",
        "outputId": "798efc99-ae02-4407-ed53-e8217a1cedb7"
      },
      "source": [
        "print(\"ARIMA(1,1,1):  \\t LL = \", results_ar_1_i_1_ma_1.llf, \"\\t AIC = \", results_ar_1_i_1_ma_1.aic)\n",
        "print(\"ARIMA(1,1,2):  \\t LL = \", results_ar_1_i_1_ma_2.llf, \"\\t AIC = \", results_ar_1_i_1_ma_2.aic)\n",
        "print(\"ARIMA(1,1,3):  \\t LL = \", results_ar_1_i_1_ma_3.llf, \"\\t AIC = \", results_ar_1_i_1_ma_3.aic)\n",
        "print(\"ARIMA(2,1,1):  \\t LL = \", results_ar_2_i_1_ma_1.llf, \"\\t AIC = \", results_ar_2_i_1_ma_1.aic)\n",
        "print(\"ARIMA(3,1,1):  \\t LL = \", results_ar_3_i_1_ma_1.llf, \"\\t AIC = \", results_ar_3_i_1_ma_1.aic)\n",
        "print(\"ARIMA(3,1,2):  \\t LL = \", results_ar_3_i_1_ma_2.llf, \"\\t AIC = \", results_ar_3_i_1_ma_2.aic)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ARIMA(1,1,1):  \t LL =  -27603.66641276839 \t AIC =  55215.33282553678\n",
            "ARIMA(1,1,2):  \t LL =  -27600.081863151576 \t AIC =  55210.16372630315\n",
            "ARIMA(1,1,3):  \t LL =  -27590.424032629428 \t AIC =  55192.848065258855\n",
            "ARIMA(2,1,1):  \t LL =  -27599.80748785492 \t AIC =  55209.61497570984\n",
            "ARIMA(3,1,1):  \t LL =  -27592.05537171072 \t AIC =  55196.11074342144\n",
            "ARIMA(3,1,2):  \t LL =  -27590.660808978784 \t AIC =  55195.32161795757\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "id": "gZF6IBAnlgF-",
        "outputId": "88ad50be-3792-4187-cb6c-8a6c5ce045a0"
      },
      "source": [
        "df['res_ar_1_i_1_ma_3'] = results_ar_1_i_1_ma_3.resid\n",
        "sgt.plot_acf(df.res_ar_1_i_1_ma_3[1:], zero = False, lags = 40)\n",
        "plt.title(\"ACF Of Residuals for ARIMA(1,1,3)\", size=20)\n",
        "plt.show()"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 499
        },
        "id": "XZ8AasOqli8V",
        "outputId": "b17ab2f5-c913-46db-983e-9a378952eab8"
      },
      "source": [
        "model_ar_5_i_1_ma_1 = ARIMA(df.market_value, order=(5,1,1))\n",
        "results_ar_5_i_1_ma_1 = model_ar_5_i_1_ma_1.fit(start_ar_lags=11)\n",
        "model_ar_6_i_1_ma_3 = ARIMA(df.market_value, order=(6,1,3))\n",
        "results_ar_6_i_1_ma_3 = model_ar_6_i_1_ma_3.fit(start_ar_lags=11)\n",
        "results_ar_5_i_1_ma_1.summary()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARIMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>  <td>D.market_value</td>  <th>  No. Observations:  </th>    <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>          <td>ARIMA(5, 1, 1)</td>  <th>  Log Likelihood     </th> <td>-27586.512</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>58.932</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Mon, 16 Aug 2021</td> <th>  AIC                </th>  <td>55189.024</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>06:11:49</td>     <th>  BIC                </th>  <td>55241.193</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th>  <td>55207.305</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</td>   <th>                     </th>      <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "            <td></td>              <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>                <td>    0.5663</td> <td>    0.690</td> <td>    0.820</td> <td> 0.412</td> <td>   -0.787</td> <td>    1.920</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.D.market_value</th> <td>    0.4011</td> <td>    0.159</td> <td>    2.529</td> <td> 0.011</td> <td>    0.090</td> <td>    0.712</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.D.market_value</th> <td>   -0.0445</td> <td>    0.016</td> <td>   -2.856</td> <td> 0.004</td> <td>   -0.075</td> <td>   -0.014</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L3.D.market_value</th> <td>   -0.0543</td> <td>    0.017</td> <td>   -3.163</td> <td> 0.002</td> <td>   -0.088</td> <td>   -0.021</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L4.D.market_value</th> <td>    0.0586</td> <td>    0.019</td> <td>    3.069</td> <td> 0.002</td> <td>    0.021</td> <td>    0.096</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L5.D.market_value</th> <td>   -0.0581</td> <td>    0.014</td> <td>   -4.118</td> <td> 0.000</td> <td>   -0.086</td> <td>   -0.030</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.D.market_value</th> <td>   -0.4213</td> <td>    0.158</td> <td>   -2.659</td> <td> 0.008</td> <td>   -0.732</td> <td>   -0.111</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>          -1.7609</td> <td>          -0.0000j</td> <td>           1.7609</td> <td>          -0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>           1.4633</td> <td>          -0.8605j</td> <td>           1.6975</td> <td>          -0.0846</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.3</th> <td>           1.4633</td> <td>          +0.8605j</td> <td>           1.6975</td> <td>           0.0846</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.4</th> <td>          -0.0790</td> <td>          -1.8393j</td> <td>           1.8410</td> <td>          -0.2568</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.5</th> <td>          -0.0790</td> <td>          +1.8393j</td> <td>           1.8410</td> <td>           0.2568</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           2.3734</td> <td>          +0.0000j</td> <td>           2.3734</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                             ARIMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:         D.market_value   No. Observations:                 5020\n",
              "Model:                 ARIMA(5, 1, 1)   Log Likelihood              -27586.512\n",
              "Method:                       css-mle   S.D. of innovations             58.932\n",
              "Date:                Mon, 16 Aug 2021   AIC                          55189.024\n",
              "Time:                        06:11:49   BIC                          55241.193\n",
              "Sample:                    01-10-1994   HQIC                         55207.305\n",
              "                         - 04-05-2013                                         \n",
              "========================================================================================\n",
              "                           coef    std err          z      P>|z|      [0.025      0.975]\n",
              "----------------------------------------------------------------------------------------\n",
              "const                    0.5663      0.690      0.820      0.412      -0.787       1.920\n",
              "ar.L1.D.market_value     0.4011      0.159      2.529      0.011       0.090       0.712\n",
              "ar.L2.D.market_value    -0.0445      0.016     -2.856      0.004      -0.075      -0.014\n",
              "ar.L3.D.market_value    -0.0543      0.017     -3.163      0.002      -0.088      -0.021\n",
              "ar.L4.D.market_value     0.0586      0.019      3.069      0.002       0.021       0.096\n",
              "ar.L5.D.market_value    -0.0581      0.014     -4.118      0.000      -0.086      -0.030\n",
              "ma.L1.D.market_value    -0.4213      0.158     -2.659      0.008      -0.732      -0.111\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1           -1.7609           -0.0000j            1.7609           -0.5000\n",
              "AR.2            1.4633           -0.8605j            1.6975           -0.0846\n",
              "AR.3            1.4633           +0.8605j            1.6975            0.0846\n",
              "AR.4           -0.0790           -1.8393j            1.8410           -0.2568\n",
              "AR.5           -0.0790           +1.8393j            1.8410            0.2568\n",
              "MA.1            2.3734           +0.0000j            2.3734            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "g0XZgxomllbE",
        "outputId": "29393271-0063-4506-8104-9e0088b047d0"
      },
      "source": [
        "print(\"ARIMA(1,1,3):  \\t LL = \", results_ar_1_i_1_ma_3.llf, \"\\t AIC = \", results_ar_1_i_1_ma_3.aic)\n",
        "print(\"ARIMA(5,1,1):  \\t LL = \", results_ar_5_i_1_ma_1.llf, \"\\t AIC = \", results_ar_5_i_1_ma_1.aic)\n",
        "print(\"ARIMA(6,1,3):  \\t LL = \", results_ar_6_i_1_ma_3.llf, \"\\t AIC = \", results_ar_6_i_1_ma_3.aic)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ARIMA(1,1,3):  \t LL =  -27590.424032629428 \t AIC =  55192.848065258855\n",
            "ARIMA(5,1,1):  \t LL =  -27586.51188811041 \t AIC =  55189.02377622082\n",
            "ARIMA(6,1,3):  \t LL =  -27583.56532042454 \t AIC =  55189.13064084908\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 594
        },
        "id": "3z-j5ec1lsX2",
        "outputId": "e50dceaa-2f3d-4bfc-936a-9b7557ad22d8"
      },
      "source": [
        "df['res_ar_5_i_1_ma_1'] = results_ar_5_i_1_ma_1.resid\n",
        "sgt.plot_acf(df.res_ar_5_i_1_ma_1[1:], zero = False, lags = 40)\n",
        "plt.title(\"ACF Of Residuals for ARIMA(5,1,1)\", size=20)\n",
        "plt.show()\n",
        "print(\"\\n\")\n",
        "plt.plot(df.res_ar_5_i_1_ma_1)\n",
        "plt.title(\"Plots Residuals for ARIMA(5,1,1)\", size=20)\n",
        "plt.show()"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ev//+qzaOyZrJu7oa07htMwHBUPIcUU5ODuf27OxsANCrzs7T0xOzZ8/G7Nmz8ejRIyQlJWHTpk1Yt24dCgsLeTWCqpJIJGjatCmWLl2K1NRUbN26FZGRkejbt6/SdcyZM4etStHFyckJU6dOxdSpU5Geno5z585hx44d2LVrF1JTU/HXX39pPFb+flwPOUDz5ykSiVBZWcm5jas/9pYtW/DkyRP2Iabo0qVL+PPPPzWmUdWwYcMwbNgwFBYW4tKlSzh48CC2bduGiRMn4p9//jGqtODu7o6nT5+isrJSraRZVVWF/Px8zntIV4cHLrdu3cLVq1cBAKNGjdK43+bNm7UGOrFYjICAAHz++efIysrC/v37sW7dOt73jyofHx+2e6mbmxvat2+PVq1aaT3myJEjbAmvZ8+eGvfbtm0b3nvvPfZveUakoKBA72pYHx8fZGZmorS0VK/jLE2e6TOkRClnM20IhnrppZcAyBqpuAbOyLtAtm7dmn1NnoOqrq7Wef6goCCMGDEC69atg4uLi1r1j77EYjHmzJkDQNb7Rp4GeaPq+fPnDTpvQEAAhgwZglWrViEoKAgXLlzQWjRt3rw5nJ2dcfPmTc7Sk6a+1Z6ensjNzeUMClxdch89egQA6N+/v9q2c+fOaUyfNh4eHujVqxe+/vprREdHo6CgwOBzyYWEhEAqlXJ+/ufOnUN1dTV7rxlLXjqIiIjA8OHDOf9zcnJCfHw8nj17xuucsbGxcHBwQFxcHIqLiw1O24gRI1BRUYG8vDxejcnydpU+ffpwXoe8BLR161YorgYsz9nLq0D5Kioqwv3799mBYbXJgwcP4OXlBX9/f4PPQQFBB39/f3Tv3h2pqalYs2aN0rYrV64gPj4enp6e6NevH/u6vMFV3rClKCUlBSkpKWqvy3OPQvRlbteuHfr06YP79+9j586dAGQNueHh4Th48CDbY0TV7du32Rx9Xl4eZzVbSUkJSkpKYGdnx9mmImdvb4/Bgwfj2bNnam0W165dw+7duzmPa9OmDaqqqtT62m/fvh0XL15U21/+o1UNMDdu3MCvv/6qMX2qEhMTwbW8uLxtxdjv5Y033gAALF26VCnnWVpaynY3Va3XNkRZWRl2794NiUSCJUuWYMGCBZz/9e/fHyUlJdizZw+v8zZs2BAjR45EQUGBUaNhu3Tpgp9//hlxcXFqnRtUpaen48SJE/D09MQPP/zAeR0LFy5Ex44dkZKSojQ2Rt5Wc/nyZbXzZmdnIyMjQ+31Z8+eITY2FuXl5ejWrZtataZ8Dix9xoFoIh9TI9RcXikpKcjJyUHnzp0NKlXKUZURD19++SXefPNNLF68GKdOnUJoaCg7DkEsFuObb75RKu6HhYXB2dkZa9asQUFBAXtjxcTE4Pbt25gyZQratGmDFi1aoH79+sjLy8Phw4dRWVmJSZMmCZLmDz/8EEePHkVcXBwGDx4MBwcHLF26FOPGjcOcOXOwdu1atGvXDu7u7sjIyMCdO3dw584dbNq0Cb6+vsjMzMSwYcPQqlUrBAcHIyAgAMXFxTh69Ciys7MRExOjs5rs448/xpkzZ7BmzRokJyez4xD27t2Lnj17IiEhQe2YmJgYbN++HfPmzcOZM2cQEBCAmzdv4vLly2wjt6KhQ4di1apV+Oabb3D27FkEBQXh0aNHOHr0KF555RXek5pNmTIFLi4uCAsLQ2BgIBiGwfnz53Ht2jW0bt1a55gLXQYPHozDhw/jn3/+wcCBA9GvXz92HMKTJ0/w2muvYciQIUa9ByCbQqSwsJCtC9dkxIgR2LVrFzZt2qSzHl/u3XffxdatW7F69WqMGTPGoCo0kUjEVmPqsnXrVlRXV2PIkCFaG55HjBiBCxcuYNOmTez4li5dusDDwwMnT57Exx9/rLT//fv3MX78eISFhaFp06bs/X769GlkZ2ejcePG+Prrr9XeRz54ULWhOS8vD4sXL2b/lpec58yZwz6cJ02apDSaX9O5AChNrikv4SxZsoRtWxw+fDjCw8OVjpG3C3KVlPVBAYGHxo0bY9u2bfj5559x/PhxJCUlwdXVFT169MB7772nNqGUp6cnfvzxR8TFxWHHjh1sQ+2QIUMQGhqKyZMnIykpCSdOnMDTp0/h4+OD1q1bIyYmRq23hKFeeuklvPLKKzhw4AA2bdqEmJgY+Pv7Y9u2bVi3bh0OHDiA3bt3o7q6GvXq1UPLli0xZswYtk5X3pc+KSkJZ8+eRX5+Pry8vNCsWTNMnz5dZ+4OkNXFbtiwAcuWLcORI0eQnJyMZs2aYd68eQgMDOQMCC1btsQff/zBdgmUSCQIDw/Hxo0bcfDgQbWA0KBBA6xfvx5LlizBhQsXcPLkSTRv3hxz585F165deQeE6dOn4+TJk7h+/TqOHTsGR0dHNGzYEDNmzMCbb76ptTTE17Jly9CpUyds27aN7dbYokULTJgwQamLsDH4jvyVDwZLTk7GzZs3lQZQalK/fn28+eab+OOPP7By5UqTzgoslUrZrrq6Sk4DBgzAggULkJCQgNzcXPj6+sLZ2RnR0dFYs2YN7t27p/QwbtKkCYYPH45r164hISEBRUVFcHJyQrNmzfD2229rzOzcuXMHrq6uatNvlJSUcPaYk5fOAVmPKMU03LlzB2KxWG3SPQCc5zpw4AD774iICLWAsHPnTvj4+BgdEEQMVzmZEEJquZSUFLz66qsYPXo0Pv/8c6POVVhYiM6dO2P8+PH49NNPjToXwzDo0qULunTpgh9++MGocwGyTgRDhw7FRx99ZPA4ETlqQyCE1EmNGzfG2LFjsXnzZqMGawGyzhh2dnYYP3680em6c+cOCgoK2BHbxvrxxx8REBCACRMmGH0uKiEQQuqs4uJirF69Gl27djV42g1rVlpailWrVqFTp07o3Lmz0eejgEAIIQQAVRkRQgipQQGBEEIIgDrQ7TQ//xmk0tpV6+Xr64bcXMNHe9Z2tnz9dO107ZYmFovg7c09X1qtDwhSKVPrAgKAWplmIdny9dO126bacO1UZUQIIQQABQRCCCE1KCAQQggBQAGBEEJIDQoIhBBCAFBAIIQQUoMCAiHEqqTnPsOERQm4l/bU0kmxORQQCCFW5do92ap9STeyLJwS2yN4QPjpp58QHByMO3fuAJAtYTdkyBBERUVhwoQJSouua9tGCCHEvAQNCNevX8fly5cRGBgIQLbq0cyZM/HFF19g//79CA8Px5IlS3RuI4QQBtY/sreuESwgVFRUYP78+Zg3bx77WnJyMhwdHdnl3kaPHo19+/bp3EYIsWFGLBJPjCPYXEY//PADhgwZgkaNGrGvpaeno2HDhuzfPj4+kEqlKCgo0LrNy8uL9/v6+mpf6N1a+fm5WzoJFmXL10/Xrp2bmyMAwMXZoU59VrXhWgQJCJcuXUJycjJmzJghxOn0kptbXCsmjVLk5+eO7OwiSyfDYmz5+unadV97cXE5AKCkpKLOfFbW9L2LxSKNGWlBAsK5c+dw79499O3bFwCQkZGBd955BzExMUhLS2P3y8vLg1gshpeXFwICAjRuI4TYLqowshxB2hAmT56MkydPIiEhAQkJCfD398eqVaswceJElJWV4fz58wCAjRs3YsCAAQCA0NBQjdsIIYSYn0nXQxCLxVi8eDHmzp2L8vJyBAYG4rvvvtO5jRBCaldFcN1gkoCQkJDA/rtDhw7YvXs3537athFCCDEvGqlMCCEEAAUEQoi1oVZli6GAQAghBAAFBEKItaJWZbOjgEAIsSpUY2Q5FBAIIYQAoIBACLFSNNup+VFAIIRYFZHCbKdShkHO01ILpsa2UEAghFitfxIf4dP/dwbpuc8snRSbQAGBEGK1bj0uAADkPi2zcEpsAwUEQgghACggEEKsFAMADDUsmxMFBEIIIQAoIBBCrBmtr2xWFBAIIdaJAVUZmRkFBEKIVeEsFFBBwSwoIBBCrB8VFMyCAgIhxCpRDDA/CgiEEOtHVUZmQQGBEGKVpFIGz8qqLJ0Mm2Jn6QQQQgiX41fSLJ0Em0MlBEKIVaHaIcuhgEAIIQQABQRCCCE1KCAQQqwLTVdhMRQQCCGEAKCAQAixMlQ+sBwKCIQQQgBQQCCE2CiplMHNh3mWToZVoYBACLFJexIf4buNl3H9AQUFOQoIhBCblJlXAgAoKC63cEqsBwUEQohZZOQ+Q/KDXIOOfVpcIXBqCBcKCIQQs5j0zSEs23RF944c3YxW7bkpeHpoMTZ1FBAIIYQAoIBACCGkBgUEQohVMd/ANKozUkUBgRBCCAAKCIQQKyMy2+R2NEmGKgoIhBCrwpit+w9VGakSJCDk5+dj0qRJiIqKwuDBgzFlyhTk5clG/12+fBlDhgxBVFQUJkyYgNzc5/2QtW0jhBBzoNm2nxMkIIhEIkycOBH79+/H7t270bhxYyxZsgRSqRQzZ87EF198gf379yM8PBxLliwBAK3bCLEGVdVSzPktEVfvUUbFnMxXZURUCRIQvLy80LlzZ/bvsLAwpKWlITk5GY6OjggPDwcAjB49Gvv27QMArdsIsQb5ReVIzy3BugO3LZ0UYgJUYaTOTugTSqVSbNiwAZGRkUhPT0fDhg3ZbT4+PpBKpSgoKNC6zcvLi/f7+fq6CZp+c/Hzc7d0EiyqNlx/tViWXxJLxIKmtzZcuyn5+bkjK78E7i4OcHZUfwS5uTlpPE5ITo72AAAPD2ezfCe14XsXPCB89dVXcHFxwZgxY3Dw4EGhT68mN7cYUmntivV+fu7Izi6ydDJ4eZxZhIt3sjGsR3MAQLVUChFEEIsNL9bXluvPKygFAEirpWrpvZf2FBm5JejeJkCvc9aWazel7OwivLMoAU3qu2HehAi17cXFZRqPE1JZeSUAoLCwVNBzZxeU4sz1DAzu1pSt/rKm710sFmnMSAsaEL799ls8evQIv/zyC8RiMQICApCWlsZuz8vLg1gshpeXl9ZtxHp8teY8qqUMhnRvBrFYhCnLT8DRQYLvp75s6aRZ1II/LwCA3gHBFlVVSzlff5xVbOaUmMf3W64gPbcE3Vr7o56Xs6WToxfBup0uW7YMycnJiIuLg4ODAwAgNDQUZWVlOH/+PABg48aNGDBggM5txHpUy0tfNQWC8spqFD6ruzNPSqUM+wCrXeVO6zX1hxP4YNlx9u+lGy9p3X/1P7dMnSQlIoHHI1RW1d77R5ASwt27d/Hrr7+iadOmGD16NACgUaNGiIuLw+LFizF37lyUl5cjMDAQ3333HQBALBZr3EasT1l5FVyc7C2dDJOb+3sSUnOe4ffYSEsnpc4or6hW+vv6w3wLpcQ8KmoCwq5TD/DOwJcsnBr9CBIQXnjhBdy+zd0To0OHDti9e7fe24hlSRkGE789wv69/uAdTBrc2oIpMo/UnGcAgMJnFTSO1QAFxeV4nFmMti18LZ0U3UyUhS8rrwIAnLqWgeG9W6K8srpWNCgDNFKZaCAv9so9K6sy6fsVl1bicaZ1NLoBsqoyeXVZpYY6cKJuwZ8X8P0WHmseGKmqWopqqUDfi8CRXzHOfLziJGJ/OSPsG5gQBQTC6f2lx5T+Vp1N4GFGoaDv983aC5j3xzlBz2mshAtPANBqXfrILZT1EJq0+AjO38oy2ft8sOwYpsedNtn5bRUFBGKQy3dzBD1fRs36tkI6cTXNqIdSWWW17p0Ip2opgx0n7pvs/FXVjNV2bqjNVY0UEOq4RxlFKDFxdY+i/KJynZOTFT6rwIN0YUsYXP7Yews/70w26FiaPYHYIgoIdRjDMPhy9Tks33JZ8HMXPqtQy9Wn5z7D9LhT2J+UovXY2LiT+GrNecHTJKTcwjKlnF5eIfdgKaKdtebiTak2djeVo4BgA+6lCp8bP3o5DbNXJiq9ll0ge2jeeJSn9dgUlcbj6w+e778/6TEqeFbVFBSXI6ugFJl5JTh2OVVpW1pNbyFDyQeeye0+/dCo89kqIaeyvnovFwfPpeDWI2G6rQr94L77pADzV59T65BRmwg+dQWxfqXlVbj75KleXQMZPX8+ZRVVkIjFsLfTnucofFaBpZuel2A2JfyLp88qMLJPS53vMfPn06iWMnB2lKC0vBq9wgLZbZpGxxLzeVZWJSmGbZYAACAASURBVOjMpVy9lwqfVcDD1cGo895NKUDX1v5GnQMA/i/+Bpspqq2ohFCHaXqE/773Jr7fcgVZNXP18DoXo94VVZsPlh3HxytOYu2B2xofzpMWH0HCxSdqr5eWc7d5VFVLsf7gHRSXyuagkXcLLS3XXqIwtEdUbS7681VZVY0JixKw7+xjwc9dXFJp8raYaStOGn2Oo5fTdO/Eg9nW9TEhCgg2KCNXVvdfUaH+IC0qqcCh8+ptANcf5OHdJUf1ep+S8iocuZiKi3eyObdXSxnsOvVQ7XWuZ0hpeRW2Hr2HwxeeYHPCv3qlY/Ve46dCqKttzPLxJfuShA8IDBirXttAtTqrqlqKE1fTMGFRAp4WlxtwPqFSZjlUZWSD2PuW47f6W/wNJN/X3gbA48zGUXmISKUM5q8+h8z8mtlH9fzlpWQV49LdbLR/wU+v405eTddr/9qIfWCb4mnG45RV1VLYSawjX/q//zvL3mNpuSXwdHPU63ht92XyvRz4uTtAbMUBEqASgk2S54y4bs1npcZ3URVysrDU7GJMXHyE/aFqo6kBkwGwYts1ncfbQgBQJf+m9J1Bnqvh/36actUcA93ddyd/d5R9kK7Zdwu3H5tvniPV0gufe8xQs34+ZZJqOaFRQKjLdP3ITZRbkapMKSASiZBTUKpX180TV9Lw2+7rOMhRfaUpI2ZsHvfP/eadZdMaGHIL3Et9iveWHlNbWvTaffWlRvlkDs4kZwAAjl1Ow7d/aZ8JVUiKGYgD57R3lRZCeq72nm+X/81BzlP1oFRUUoG9iY8E7bGlCQWEOubUtXScvZGp9npVtRRfrTmvVJ9vqsKr6myWSTcz8ekvZzDjZ35TDYgA/PHPLZy5nmn19bJX7wk7Ytvc5LlkeUM9H3efPAUA3HhoaNWishINnQjMaePhu5yvV0ulyOQYRX/xTrZaW4Ox+asft17FF6uS2L9Lyirx5/7bWLnrOrYevcd+7qZEAaGOWbXnJn7ddV3t9SnfH8eD9EL88neyoA/ZfWcfo7JKey+fC7efByFepQRDf1gK18U1EvqpjkFSVdW6P5gn2cWYsCiB/fv7LVf5p8/KZeaXIG7HNYP70Rucg7XSoH86OR2TFh/FrJWJaj3y5L3jnmQbN95FVVlFNXvv7j79EEcvpbIZrGozrAxJAcFGVFTWLNrBPP/9CVFjtPnIv9h9+iHvuY34lBIUk8X1E+AqVsv2fb73kUupats/FqCLYtJN9dJXbaZ4DyxcewEXbmfjTkqBWdNgpfEA/xd/k/23ECOuKyqlal2wD194ggmLEpRmbv1qzXlUVUsh1GSu+qCAUIfpO5jMUP8kPsaP267izHXzPCz5FJ31bdjWWf1R8+S09iosVffTCpH7VHOpTPFzKizhV22kT0aCV48wgT7UzHz1qp2qain+SXxk9EDFa/dytX6OfJy7lYW5vycpvbb12D0AzzNscpa6z6jbqS2S9zISqFFZXpTN0WOgmykwjKxKavvx+6jSM3t1o46u4vX1n7I5ozStAMd5Cxh4W3DdT3wba/Vpw+CSdDMTv/x9HdNGtEPbFr5Ys+8Wrt7LRavGXjh7IxMMgNe6BPE+n+qV7D79EIcuPEHcxz1RWFLBeb/w+djSc5WDlvwY9QDAERGoUZmYAltlxLHNmBhxL02YOZOM6ba6/uAdnE7OQKqGut0nBi7sfuOhbGCeOWeOrW242hCKS3RXtTAA/p+Bs9LKPcyQzY91/UFezdxWacgvKmc7WJRVGP+9yUfQX/nXuI4EpeVV2HL0X1RVS61uVl0KCHUYV4aiWsogq6a/9a5TD/DT9mtssf5xZpFaX3KL0NWIYIQvfk9CfpH+o1Cz8ktRWSVFSrZhAaU2EfIZxefrYxgYXR0jbwg/eD4Fs1QmXQSA+NOP1NZ21iZbS2lXdXBZcWklthz5l3ej765TD/BP4mOlIPhIZcLHRDNVv6qiKiMbJq/zv3A7G7lPy7D5iH5TQpiKwZ2MGPUfK5eSskp4uyuPQrW2nBoAHL2UipAgbzTwcbF0Ugz2KIPfsqj5BkwVIXf0UioOX1CfE0stLZlFaNXYi9c5//hH85gUqcqDf9PhuzhVM5aCj4qa4HXpbg6cHWWP4O82KI+/OJWcgaAG5l+HmQICMbq4bgn/pnI1LDMGPdhLyir5d+nTsFtWQSl8PRwhEQtT6GYYBn/uvw0XRzv89HFPQc7J/T789pNKGdxPK4STo0Tt2NuP8/HtX5fQoZX61CAPeQYEY6aM/nP/bYOOM6RK/mFGoVqw0HcqFUWaJnIELJNJoYBArJqmnlLFHD1iqqUMzt/mnkhPmynfnzAqPXmFZYj95QwGRDTByEjd03brwxoGbQGyag75RISRHQKVtl28I6tTN3Sgmrl6w51OzkCrxl5GzZ80fzXXwk56Prl51qNxxZmbj/JRUlaJjsH19XtPnqgNQWAMwyDxRgbNx28MHr+vXI4BbluO3jNBYpRxLTYkH/B2U6CFWwDT9c2/+Sgfa/Zpn6KD6+N/nPm87UQ11y8Ry45QrUqxNsevpOFe2lNM/u4o52h+Q525zr+6COD/3d7imNfpuw2XELcjWW3sglAoIAjs6r1crNx1AzuOm26BcT7yi8px6LzuelVrpNjLqEBDA/D6g3fUXtM0zbaq1ftuITO/RJCeJwDYxkrVnC7DMGaZf0bu5x3X8M/ZR1r3+W7DJRzTY/7/a/dzcU+lek7e8UB+vaKap0iFgdU+fAc1CkG+Ep5QAUFxcSchFZZUIkWlR5zqSHvVsQtCoIAgMHkRP8+AnixCmh53ymoaifWlmNNUnRdJG4ZnDvVeaiFm/ZqIOb+d1TttXOQlk8eZxShU6Gb5zrdH1BoLAWDDobv4iyOgGev87WxsOSJMKUkqZVBZVY3lm69gwdoLnPvIq+2Mnd3WHHP0qLpsZNdRo/DIJHCNy1i5+4YpUqOEAoLAxOyIVmFzhlXVUo1ryUoZBgfPp3DODFobHeZYRY0PviNt5fKLygX5nhTnTZr240mlqR9uPS5ARWU1/tx3CyVlsvQdPJ+CQ7p6xVi49uX7LVfw7pJjWvdJrMllW2MPLT64qh2thbED9QxFAUGDzLwSg+Yvkf84hK5O/fvkAyzecImzd835W1nYcOguNhzinrGRmJdqn/JjV9Jw9HIa/j75UPD3qpZKedclq05PffdJAWeD7r+pT5H8gF8D8YRFCdhzRns1lbWy1JgboZbsNAUKCBrMWpnIe7pmRaYqIciXvSwoKsfB8ylKA3lMUZdIDLfh0F2lh2+Zlp5CUimDcoXFZq4/zMPtx/m8e97M+Pk0/rvsuM79Lt/NwfLNzxepv3Q3GwvXXcSRi+qTAFq0OoXwZormKQoIWhjSU8hUKxKKanpyFBSXY8Ohu/jslzPstmdllile1gWmqplRfPjuOPEAgHrVyvlbWfgt/gbeX3qMzeUv3XhZ6yIxNx7mIfHG814tT4srNDbm3lToBvrjNuVpurcdk3V62M7R+YFrTMZ9junESd1DAYEHhmGw88R9XnP5yyf4ungnG08EnOagJh6wc/ZLGQaX7mQjI6+EurgaYeK3Ryz23j/vTGZ7u3z4g/JYCMUMhWL//iUbL2PlLvXGRa57U9ugsLQczfP4K3YxlRNi+mciLFO03dhsQCgpq1QbJbg/6TEmf3cEF25nKb0ef/ohdp16iF/+Vl54RiplsGrPDY0Pfnkucd/Zx3isUK+8bt9NHNQwC2RpeRXnfPTimohQqfDwX7H9GmavTMRRjrn/Se1SWq48z47iPbVko3rXRqmUwfErz+uiVadVPnk13SzjMojlmKLKyGZHKstHpw57uRn6hjeCs4MdNiXIumnG7Xg+lcO/qU/ZIn95ZTXSc5/B290RTg52SM8rwalrGTh1LQNzYjqiRaAnu5ISAHYSNXn3z1GRLREV0QSbarocvtKpsVq6ft6ZjOsP8rBiWg+4Otmzr8vbJrjGN+QWWraLK+FHnxKj6ojYa/dzsbtmpDAgW1hlg8Kyj89UZmG9UsuX9iSWYZMBQXEd3J0nH+D87Sw00TCR1Lmbz0sLKVnFmPPbWbQI9MCcmHClhuPkB3loEeiJp8XKRWvFFbY2JfyLHm0D2L8rq6px4mo6fNydsDfxEVKyi+FoJyu0HT7/BI0buKFloCeKSyt5TdpGrNuNh/moqNQ846a29SQU2yQAaJ2xddLiI2ZZbpFYmvDfsU0GBNV1cJ9kP9O4NipX33759AXVCmvwVlVLMXtlIjJUFuRWq2ZS+A65+nk71ASEnScfKL3eroUvZ/pI7XJOywjZTxU6CuiSV6S5PYuCATGUiDHn2HoTyM0t1nsOFcVF0g31zsAQ7D71kF18283Z3mKDSQghtuenaT3golCtzJdYLIKvrxvnNpssIQhh1Z6bSn9TMCCEmJMpcvI228uIEEJqMxqYRgghxGQsHhAePHiAUaNGISoqCqNGjcLDhw8tnSRCCLFJFg8Ic+fOxVtvvYX9+/fjrbfewhdffGHpJBFCiNUzRX8giwaE3Nxc3LhxA4MGDQIADBo0CDdu3EBenmFL8RFCiK2oc43K6enpaNCgASQS2cLdEokE9evXR3p6uiWTRQgh1o+mrlCnqT8tIYTUZb6+bvBydxT0nBYNCAEBAcjMzER1dTUkEgmqq6uRlZWFgIAA3QfXMGRgGiGE1HY5ucWoLNN/FlptA9MsWmXk6+uLkJAQxMfHAwDi4+MREhICHx8fSyaLEEKsnwkalS1eZTRv3jzExsbi559/hoeHB7799ltLJ4kQQqyeKepFLB4QWrRogS1btlg6GYQQUqvQSGVCCCEmQwGBEEIIAAoIglkwqTMCfF3Yv//vsz54f1go+3d9L2f051ghDQAcHSQmTx+p2xr5uVo6CcRE/H1cOF+vcyOVrcm88Z30PuaTUe3QwNsZACASieCk8GAXi0To9GJ9pf07tPIDAIQ09UGgwg844sX6kIhpRTRiuD4dGrH/Xjmzt+USQgT3wbBQTHm9jVneiwJCDdUlNBe/11XpAc+lvEKKqM5NAABebg46G3nsa1ZDq6yqxlfvdGZfd3W2x2+f9lHb//fYSPbfvcIaaj85sWl92gey/7aT0M+6LpFIRHB3UV8IhxqVBcKneF3PyxmDujVl/25Y7/kxX03sjNDmPght5oPeYYH4PTYSTg52aOSnPtjD1UnWkYsBwwaEiiqp0j6DFd6Hi6ebA8YNeFFnmknd0bKRJ97s+4LSawG+Lpg/IcJCKbItw15uZukkKGkR6GmW97HJgPC/ceG89uvZ7nmufHRkS/bfgfVc8cnIMLW6/zH9W2l9r/peznB1ssPYV0MAAL4esmHnzo6ae//OHtMRc/+juzrLzVn/pfSIecW+3YH3vt1a++MVhTaniJD6+HpiZzSq74b3hrbWefx/XlXPQBhSLWqrBnVvaukkKBGL1KuUGROMRLDJgGBvJ9H6EJZTfMi2biYbPa2t6sbBXr2KyclB9j4tGnrCwV6CFdN6onOobGqOz8eG6wxOLRt5wstNfb6SdwaGKP2tz8OGWEarxl68922pkiN8b2goRDUPhYiQBjqP79raX+011WpRQyhmggJrcUO2rgwU1wPYUjRWDVGVkXA+H9uR/Xfcxz017vfpm+2x+P2uEIlE+L9P+2BsVLBe7+Ph6oB54ztx5tg83RzRLMCD/Xvufzrxbjzq3iYAg7oFsX9rau8ICfLWK71EGFzVh9qM6N0CCyY9b1dSfB51ba09ADSur/5epnqetW3uy/771c5N8PXEzlr2tl6m6KFjKmaMB7YbEAJ8n+dutJUWXgzyRj1PWU8isVjE5tL00aSBO2fpQVWQvzvbE4kPR4VzarqG8a9R24Ml/G9cR6W/5Q/OVyKaKLVhBfnLcu1S1QdUzX22cmZvvDPoJa3vxZXZ0OSX6b147wsALzZRLtXUr+lVJ6fYtlabVNemCTE1BC8KCAQAd7dCZ0c7DKjp8aTIx8PJDCkiin6d0Qv2dhK2l1iTBm7sg/PDUe0x/x3duWp5L2Q7iZiz+uK9oa3ZTABXryKxhm7MfDImit4d8ry9YkSfFkodIGpRJluNWgAmACggcHKws/zHoq0covoA6NtR1gd9ZJ+WWDmzNzs2Qtt5rKiKtM6xt3v+0P32va747C3N7Tvyr0Hf51NESAMs+aAbJg4K4awyUgwi3hrmzFfs1qyJp0L71audg/QOKObGp0T83+g2CG6suyp1/jvC9uga2DVI904cNN4adXG2U2vyRq/maODtgnCVAWX6WPJBN5RWVBuVjg/faIuAetyjE7koBjA7iRgL3+2KCYsSAEBjFdfc/3TC9Qd5KKuoxu7TD41Kb23l4WKPwpJKk76Hn5ez1u3y74cB4Opkr/a6Ns6OdugW+nztkA/faIsGPurv99HwtkpVpEKprZnsBj7OvDJEQjcsv9GrBY5dTkNxqfo95+nmgKfFGtY20PA5U5WRwFyd7ODp6sD+PbBrU6OCASCrogk0sl417IV6aOCtOyAY0p4hJxaL8GqXIHgoXL+tGRX5gu6d9DRrjIG9vRgGHq4OeHdIa7Rp7gs/L/2r+sJeqMf54BeJROwYGCEZ2zA7SqErtzkZ8qsZEKFeHSskbWly1dQjipbQFNYPH/WwdBKM4lzTs4hPF1pV8qkyrLXqyMlBgjIjS1ravNnvBUgksov3cHVA4TP9V55SxacKRpX885f/tju/1ACdX9LdrdTUvvhPOEQ1j6nYtzvAx0O92snY55Elb723XmmFq/fO8D/AxInVlrnTVOVnCjZdQhCLRFbV31hfPcMa4s1+L3A2Jusib3R8uQ3/5UqNoWliP0UhQd5s46sxpR998RkfUM/TNI3zhrYh8FG/prrKkJx8U38PtgdUq8ZebE87IYlMMH+XJ58Sr0jEfja1GVUZ2bgPhoUq9fqQiMV4JbyxQXPXSGoeuOZqJBzeuwV+1KNE1rOdaQOVk57X/TnP0e36CqgJgKboF6/pu503vpNVDGR0N8Ho+jbNffHh8Lb47dPeGvcxJgz5mrjXnq5pbBTRbKc2LvzF+oJVJ2jqlmgqIhG/6in5TW5MyUXbQMNfZ/TC6MiW6K5wfkuWEU39gOHSpIG7XqOmNbHGrpsikQhhLetBItb8aNN1H0aEaG5H7N3eNJNMytPUs11DTB8dhjf7aW7fklffOZogM0cBwUYJFRC0/XgU8akCEomeT9ng4mR47pGrTeXlNgGY+nob2NtJ0D+iCcRiEVu94O/jotRV15xMWWX0/rDWeLlNgN6jptu28NW9E2B0nYX1hRMZbRPJmaoqk70PwKB1Ux+8Eq65irVtc198PjbcJGOMbLpR2ZZ5uAjTu4jvg4zvz2hM/2D0C28MLzdhez8F1HNBe5VR4MFNvDHzzfZo1dgTV/7NEfT9dJn6Rht4uDrg+oM8AKaZqCzA1xUTVOa80uWX6b3YxnZdjE6xGSNCn/aBuP4wD1n5pSZ5qLd/oR4u3RXgHlL4TOa/E8HZOyygniuaN/RQe10IVEKwIW1q5qH5cHhbwUoIir/p1s18NDYe8yohQLZmBNdAK2OJNISkkCBvrdULuvRoa1jVVvsX/NCioSfsa9p/jEmDkBzsJfzTYmSxRugg2KSB5vvmjV4t2H8bcucrHjNzdJjStqAG7pj6Rlutx9vVBNmoCPXfh6ebA2eqGvm5KXU/n/J6G0x4LYQdiGoKVEKwQULmjxQn1bOXiDG67ws4cC7F6PMKnYvzNVEvobdfaYVXuwShSmWNC776dmyEotJKg3qKWZr8cT59VBgy8kqw/uAd/Y4XuISgukKh+hvW/L+uW4sjXVERTZCa8wy9whrC1cmeHdT4xX/CEeCje9yRfMT3wK5N4eJkj7X7b7PbFFdL1PaR6DPPmaGsI1tCzEqIZ62DvRjzJ0Tw6+ZnJjPfbI//Rodyvh4erOPHxOMz6R6qPqW0g70E/j4uaGRgqcbBXoKRfVqapIFQXx31fODIH+itm/mgb8dGauuDKK7iZioO9vwfYa1qJuozZNyOh6sDpo1opzSaHAC83Rx5rYku0vBvQNY4PGnwS3ixiRfneA9zooBgQ4QsojvYSdQegroCjc5nLs9IpWm3kCBvdAxWzyWGBHkLUuLQNetobddD4K6+/r78p18x1JIPurMdG7SXOBiMjQrGgkmddbefqdwqAVzXoTDliBBaNfbCp291sHjVIQUEm1R7B+MBQFSnJmZbdNy26HdfaOsHr+8024Zyc7bH2KhgdG/jr1a3vui9rkp/20nE/OZ04vGUl09l4cKztNFQz55elkJtCKRWErr/vqZGZ6KZthy5g71E54NVqDYEFyd7vDNQvfRW38sZzo52KC2vErxD04DOTfRq95k1rhNKn5Urp8/bGVn5pQKnzDhUQqij5k+IwLcqOSQhfxV8amD0WbhFH43q185FWayRMctgqt5OqreEplX8nh9v3A3JZzoUfcinsQlt7iPoeb3dHeGmUE0lP78+o5LNhQJCHdWovpvGqZc1PcyH9WiGsQP4LRHKJz/dPEC/vtJ8ztmuhS/nesFG41lAGNO/lcn6gFuCkCUj1fuqu67R5kbEgxebeGF0X2Fnq20R6IHfYyPZaiX59UgEHtVfz9MZv8dGKi2fay0oIBDWkO7N0DssEO9wDGZq01z36FV9xjYE+rny7tUypHtTALIf5tQ32pp14jtVkR0a4fOxppnXyBKM+ih11PmIxSJ4uGgecW6OcWn6XJ7qfeXv44KBXYMwRccYA0PJe5b5+5i+8Z0vCgg2xJgfoB2P0av2HJPsLZjUGe8NlU/I9/wcHwwLVR+FqeEt5PMaebk5sEHHFCN7bZExAxT5fAOGBO+WjTRPHSF/iOrb/sBnf9WPQiQS4Y1eLYyeGVVT47uvpxM+GdkOE62o9xoFBBsS1rIeAKjN22MnEQkynoBr1tUAX1dEhMgn5Hv+w+D7oGjXwldpVTE5c8+rZg3jBEyhkcJiTg15rtIn73fP6zswIN5ofSjVorb/ZVO6AwD6dNA8sji0ua9B4yJMxXpSQkwuskMgurb2h4uT8tf+8ye9lKoOeM1KyvGanR6rconY/1F8TfmFJR90g7uLPYpqlrk0ZRAY0r0pVmy7xrkt7uOedTYgyD/y8a+9yHvNg95hDbE/KcUkpbSurf2R+9QyPW+Eror0cnM0aNEkS6ISgg0RiURqwQCQ5ewVB8RwPfz4/FhU57fXtgCKSKQ7s+fj4QR7O8nzEoIBEYHvyM/2L/jhZQ3zEllTDs4asIGbVzWM5m+Z6/sc1qOZjvfm/day/fV4xpt5RnirRAGBqFGdFZSL6rTNrk52GNQtSGmfhlpGqsqql5R/gbp+vIaUEPTJ2dMDgR95SVC9/UHPgW0K//54ZDtMHvySxp5xpjA2SrlHnSlWcKttKOtjA8ZGBcPLjf8cKVy5OtVXVJ/NAzo3gb2d8sNXW6nCx8MJ7lp6oCjydHNAj7YB6NNB/7lx9Asi9EDgY2CXIFRVSxHJ4/vgesZ6ujngaXGF0k2k2IvNXM1DfiptaXW2WlAPVEKwAb3bByLshXoGH98i0EPtWdlNZaI3Pg9e+S6uNdVWr/dszuv9xSIRxr8Wgqb+z/ttW+FiXTbD0UE2IZ9qBoCbekSQd24w5CsUqRZNdXiz3wtwcpBoHST3YhMvDOneVK3EYIsoIBCtFk7ugpmj26u9PvRlWV2vQe1wAqznbIoGTQsOb6gTuD4+rukd2P00PNS1f7P6TSrXLTQAP3/Si3vd8ZqTiEQiDOvRHO4CLRpVm1GVEeH0/rBQMAyDBiqDZia8FoJG9V3h5CC7dYTMqVv6eazP+0vEIlRLqZiiS9+OjXDqWjoeZhQ9f9FKIq88U2ElybEKFBAIJ02LjTg6SJSqbuQUf1TRPZujFcfgIiGDRxOe6w/o82NXbfNo3cwH3TRMk7FsSneUV1TzPzlRw0C2VkXi9QzLJQCWz4hYE6MDwpdffokzZ87AwcEBLi4umDNnDtq0kU1NnJOTg08//RSpqalwdHTEV199hXbt2uncRqzP86pb3U91fSbtCm3mg+QHeQhu7IURfVryPo5f/bWeFJ4My6e+DA8Xe40N4+4uDnC3nhkHDNarXSBOXctASJC32d5TsRkgJMhb/b213GLyRmpBy2ZURGAZHRB69uyJ2bNnw97eHkeOHMHHH3+MQ4cOAQCWLl2K8PBw/P777zh//jxmzpyJ/fv3QyQSad1GrJAA3wvXKd4d2hoVlVJ4u1t2pShV1rQSnCm1bOQp2OAp3reIru7FZupn1DTAAxKxCK91CdK9s40wulG5T58+sLeXdR8MCwtDRkYGpFLZ+rL79u3D6NGjAQDh4eFwcHDAtWvXdG4jtYdDTZ90zkY7FVyFC1cne6sJBpQVsRJmappxc7bHb5/2MWvpyNoJ2sto/fr16N27N8RiMfLz88EwDHx8ns8tHhAQgIyMDK3biHXS9LAc0LkJBnVrikgt87XwPZel0SI5pvHu0NboFdaQ/VtX9SOveEDt+Sahs8ooOjoaaWlpnNtOnz4NiURWl7tnzx7s3r0b69evFzaFOvj61o6l6VT5+blbOgl6+e/IMPy++zr6dW2mNoDn3Te8eJ3D8VkF+29TXD/XOe3sxLzfKzzUH4cvPtF4LqHUtu+eL8WRy4rX6OfnjtBWDXDs8t8AABdnWXWcm5uTxu9M13vY20us/nNUTZ+1pxfgERB27Nih8yQHDx7E8uXLsXr1atSrJxt04u0tK4bl5eWxJYH09HT4+/tr3aav3NxiSGtZ9z8/P3dkZxfp3tHK/CcqGIUFJQYfX1wqm6ROJIKg1z9vfCfcTyvkPGdVlZT3e9VTaDcw1fdTW797PnqFBSL+9EMA2j+/0pr7oKi4jHO/ykr13lu+Hk7ILSxDkL877CVivN6zudV9jq+EN8bB8yns34rps6bvXSwWacxIG11ls7hFNAAACz9JREFUdOTIESxcuBCrVq1Co0bK1QYDBgzAxo0bAQDnz59HWVkZQkNDdW4jdZvQo4ybNHBH7/bK0yjIR6YGN9G/fpjvhHhEWbSOielYOmaoa+irvqzn6L6yHmh2YjGmvtEWgVa4aH2LQOtbAU1fRvcymjVrFuzt7fHhhx+yr61evRre3t6YPn06Zs6ciZ07d8LR0RGLFy+GuGZWTW3bCDHWC428cO1+LsJa6l7pjQiDbw9BXTOWxkQF41Ty8/bENs19tc6aSoRjdEBITEzUuM3Pzw+rV6/Wexup24T8bfuaIDdP8ySZmI75iFSnNKktq+PVhS7zNFKZ1Fo/TesBiYburoY8ROrA77lWkM+86+rMb7ZbYj4UEIjZGLLAjTYuTnweKPSUtzZREY3h5eaALhqmBSGWQwGBWAA9pG2ZRCxGt1Du1ek0eTHIG00auPGeMp0YhgICqeNqR/0z0c7Z0Q7zxkdYOhl1HnXrIXWSMaOOha7asiURIdyz5BqjfUvDF3cyp9ZNvdWmi69tKCAQUqMu9BKxtMlDWmPlzN6CnlN1jIm1cnGyx8LJXSydDKNQlRExG2vPd3u6OqB1U28M0mP6bqJMLBJBLBE2sNa2QB3doxkeZxZbOhkGoYBAzM5af99isQjTOZYLJUQfg7vzHLFthajKiJiNPA7Ya5m8TGjUHEAIf1RCIGbj5myPYT2aIaqb6XNQ1loKIcSaUQmBmI1IJMKQ7s3QqL7ppwGmkgEh+qOAQOo0KikQwh8FBEIIIQAoIJA6jqqOCOGPAgKpk6iqiBD9UUAghBACgAICIYSQGhQQCCGEAKCAQAghpAYFBFInDerWFK5OdmjZyNPSSSGk1qCpK0id1DLQEyum9bR0MgipVaiEQAghBAAFBEIIITUoIBBCCAFAAYEQQkgNCgiEEEIAUC8jQoiZ/L/PIpGZVWTpZBAtKCAQQsyiUX13ONKkg1aNqowIIVYrumdzSyfBplBAIIRYLQ8Xe0snwaZQQCCEWC0RLWxhVhQQCCGEAKCAQAixYgytgWpWFBAIIVaLwoF5UUAghFgtakEwLwoIhBBCAFBAIIQQUoMCAiGEEAAUEAghVqx5Q1oC1ZwECwhnz55FSEgI1q1bx76Wk5ODCRMmICoqCkOGDMGVK1d4bSOE2DaJWNacHODrYuGU2BZBAkJxcTGWLFmCnj2V17BdunQpwsPDsX//fnzxxReYOXMm269Y2zZCCAEAeiSYlyABYdGiRXjnnXfg7e2t9Pq+ffswevRoAEB4eDgcHBxw7do1ndsIIbaNZqywDKMDwrFjx1BUVIQBAwYovZ6fnw+GYeDj48O+FhAQgIyMDK3bCCGEWIbO9RCio6ORlpbGuW3fvn1YunQp/vjjD8ETxpevr5vF3tsYfn7ulk6CRdny9dO18yECwMDPzw32dhJTJslsasP3rjMg7NixQ+O28+fPIzs7GyNGjAAgKxUcOXIEBQUFmDJlCgAgLy+PLQmkp6fD39+frVri2qav3NxiSKW1q6LRz88d2dm2u3KULV8/XTu/a3+5bQCOXkpFbm4xJOLa3xnSmr53sVikMSNt1CcdHh6OM2fOICEhAQkJCYiKisLUqVPZYDBgwABs3LgRgCx4lJWVITQ0VOc2QohtG/NKK/z8Sc86EQxqE5MuoTl9+nTMnDkTO3fuhKOjIxYvXgxxzResbRshxLaJxSI4OdAKv+YmYmp5X0+qMqp9bPn66drp2i3NZFVGhBBC6g4KCIQQQgBQQCCEEFKDAgIhhBAAFBAIIYTUqPX9usTi2jnpSW1Nt1Bs+frp2m2TtVy7tnTU+m6nhBBChEFVRoQQQgBQQCCEEFKDAgIhhBAAFBAIIYTUoIBACCEEAAUEQgghNSggEEIIAUABgRBCSA0KCIQQQgBQQDDat99+i8jISAQHB+POnTvs60ePHkV0dDQGDx6MMWPGICUlhde28vJyzJ07F/3798fgwYPxv//9z6zXo4/8/HxMmjQJUVFRGDx4MKZMmYK8vDwAwOXLlzFkyBBERUVhwoQJyM3NZY8zdJu1McX1y82aNQvBwcF49uyZ2a5HH6a49q1bt2Lw4MEYOnQoXn/9dZw/f97s18WHodc+ffp0vPzyy2rf64MHDxATE4MBAwZg0KBBmDVrFsrKysx+XQAAhhjl3LlzTFpaGtOnTx/m9u3bDMMwTEFBARMREcHcv3+fYRiG2blzJzNhwgSd2xiGYb766itmwYIFjFQqZRiGYbKzs815OXrJz89nEhMT2b8XLVrEzJo1i6murmb69evHnDt3jmEYhomLi2NiY2MZhmEM3maNhL5+ucOHDzOzZs1iWrVqxRQXF5vpavQj9LXn5eUx7du3Z+/3Q4cOMa+++qo5L4k3Q66dYRjm9OnTTE5Ojtr3mpKSwly/fp1hGNln9NFHHzE//fSTma5GGQUEgSgGhCtXrjCvvfYauy0/P59p1aoVk5ubq3VbcXEx07FjR6t9COiyb98+Zty4ccyVK1eYgQMHsq/n5uYyYWFhDMMwBm+rDYy9foaRPRijo6OZwsJCqw4Iqoy9dvm/Hz58yDAMw+zYsYMZP368Ga/AcHyuXZGu73XVqlXM7NmzTZJWXWr9bKfWqFmzZsjJycHVq1fRtm1b7N69GwCQnp6udZtEIoGXlxd++uknnD17Fq6urvjoo48QHh5uycvhRSqVYsOGDYiMjER6ejoaNmzIbvPx8YFUKkVBQYHB27y8vMx6PfoS4vq9vLwwf/58fPjhh3B3d7fEZRhEiGv38fHB/PnzER0dDQ8PD0ilUqxdu9YSl6MXvtfO9/4tKyvDtm3b8Mknn5gqyVpRG4IJuLu7Y/ny5Vi4cCFef/115ObmwsPDAxKJROu26upqpKSk4KWXXsL27dsxY8YMTJ06FcXFxZa+JJ2++uoruLi4YMyYMZZOikUIcf179+6Fvb09evfuLVzCzECIay8uLsb69euxdetWHD16FLGxsZgyZQoYK5+MWcj7vqqqCh9//DG6dOmCvn37CpA6/VEJwUS6deuGbt26AQBycnKwatUqNGnSROu2srIy2NnZYdCgQQCAdu3awdvbGw8ePECbNm0scyE8fPvtt3j06BF++eUXiMViBAQEIC0tjd2el5cHsVgMLy8vg7dZM6GuPykpCYmJiYiMjGS3Dxo0CL/99htatmxp1mviS6hr37dvH9zd3dG8eXMAwGuvvYZZs2YhPz8fPj4+Zr8uPvS5dl2qq6sxY8YMeHp64vPPPzdlsrWiEoKJZGdnA5AVKZctW4bRo0fDxcVF6zYfHx907twZp06dAiDrfZCbm4ugoCDLXAQPy5YtQ3JyMuLi4uDg4AAACA0NRVlZGdtLZOPGjRgwYIBR26yVkNc/b948HD9+HAkJCUhISAAAxMfHW20wEPLaGzVqhBs3brC9chITE+Hm5gZvb29zXxYv+l67NlKpFLGxsZBIJFiwYAFEIsstpEML5Bjp66+/xoEDB5CTkwNvb294eXlhz549mDNnDi5evIjKykp0794ds2fPhqOjIwBo3ZaSkoLZs2ejoKAAdnZ2mDZtGnr16mXJS9To7t27GDRoEJo2bQonJycAsh92XFwcLl68iLlz56K8vByBgYH47rvvUK9ePQAweJu1McX1KwoODsbFixfh6upq1uviwxTX/scff2Dz5s2wt7eHg4MDYmNjrbL9zNBrnzJlCq5evYrMzEzUr18frVq1wqpVq3D06FG8++67aNWqFcRiWR69Q4cOmDt3rtmvjQICIYQQAFRlRAghpAYFBEIIIQAoIBBCCKlBAYEQQggACgiEEEJqUEAghBACgAICIYSQGhQQCCGEAAD+P71QkrX6vCfSAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c85JLF50l20m"
      },
      "source": [
        "### 9. Models with Higher Levels of Integration"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 337
        },
        "id": "dUkuF6y5lva5",
        "outputId": "eb1df03a-ccb9-4beb-a3f1-616c8c6bf0ea"
      },
      "source": [
        "df['delta_prices']=df.market_value.diff(1)\n",
        "model_delta_ar_1_i_1_ma_1 = ARIMA(df.delta_prices[1:], order=(1,0,1))\n",
        "results_delta_ar_1_i_1_ma_1 = model_delta_ar_1_i_1_ma_1.fit()\n",
        "results_delta_ar_1_i_1_ma_1.summary()"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>   <td>delta_prices</td>   <th>  No. Observations:  </th>    <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(1, 1)</td>    <th>  Log Likelihood     </th> <td>-27603.666</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>59.134</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Mon, 16 Aug 2021</td> <th>  AIC                </th>  <td>55215.333</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>06:13:12</td>     <th>  BIC                </th>  <td>55241.418</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th>  <td>55224.473</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</td>   <th>                     </th>      <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "           <td></td>             <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>              <td>    0.5656</td> <td>    0.682</td> <td>    0.829</td> <td> 0.407</td> <td>   -0.772</td> <td>    1.903</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.delta_prices</th> <td>    0.7475</td> <td>    0.070</td> <td>   10.652</td> <td> 0.000</td> <td>    0.610</td> <td>    0.885</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.delta_prices</th> <td>   -0.7936</td> <td>    0.064</td> <td>  -12.378</td> <td> 0.000</td> <td>   -0.919</td> <td>   -0.668</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.3378</td> <td>          +0.0000j</td> <td>           1.3378</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.2601</td> <td>          +0.0000j</td> <td>           1.2601</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:           delta_prices   No. Observations:                 5020\n",
              "Model:                     ARMA(1, 1)   Log Likelihood              -27603.666\n",
              "Method:                       css-mle   S.D. of innovations             59.134\n",
              "Date:                Mon, 16 Aug 2021   AIC                          55215.333\n",
              "Time:                        06:13:12   BIC                          55241.418\n",
              "Sample:                    01-10-1994   HQIC                         55224.473\n",
              "                         - 04-05-2013                                         \n",
              "======================================================================================\n",
              "                         coef    std err          z      P>|z|      [0.025      0.975]\n",
              "--------------------------------------------------------------------------------------\n",
              "const                  0.5656      0.682      0.829      0.407      -0.772       1.903\n",
              "ar.L1.delta_prices     0.7475      0.070     10.652      0.000       0.610       0.885\n",
              "ma.L1.delta_prices    -0.7936      0.064    -12.378      0.000      -0.919      -0.668\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.3378           +0.0000j            1.3378            0.0000\n",
              "MA.1            1.2601           +0.0000j            1.2601            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "plPI3CBFl92j"
      },
      "source": [
        "### 10. ADF Results"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aWNqsTgcl6uj",
        "outputId": "8109fda5-64fe-42e4-c7fa-d3bca6102f86"
      },
      "source": [
        "sts.adfuller(df.delta_prices[1:])"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-32.244093495707475,\n",
              " 0.0,\n",
              " 5,\n",
              " 5014,\n",
              " {'1%': -3.4316548765428174,\n",
              "  '10%': -2.5670769326348926,\n",
              "  '5%': -2.8621166146845334},\n",
              " 54845.96104221891)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 337
        },
        "id": "6ia7We0jl8x5",
        "outputId": "bf56137d-ac18-403a-aab6-037548a2ea73"
      },
      "source": [
        "model_ar_1_i_2_ma_1 = ARIMA(df.market_value, order=(1,2,1))\n",
        "results_ar_1_i_2_ma_1 = model_ar_1_i_2_ma_1.fit(start_ar_lags=10)\n",
        "results_ar_1_i_2_ma_1.summary()"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARIMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>  <td>D2.market_value</td> <th>  No. Observations:  </th>    <td>5019</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>          <td>ARIMA(1, 2, 1)</td>  <th>  Log Likelihood     </th> <td>-27614.159</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>59.272</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Mon, 16 Aug 2021</td> <th>  AIC                </th>  <td>55236.317</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>06:16:50</td>     <th>  BIC                </th>  <td>55262.401</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-11-1994</td>    <th>  HQIC               </th>  <td>55245.458</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</td>   <th>                     </th>      <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "            <td></td>               <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>                 <td>   -0.0001</td> <td>    0.001</td> <td>   -0.198</td> <td> 0.843</td> <td>   -0.001</td> <td>    0.001</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.D2.market_value</th> <td>   -0.0178</td> <td>    0.014</td> <td>   -1.258</td> <td> 0.209</td> <td>   -0.045</td> <td>    0.010</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.D2.market_value</th> <td>   -1.0000</td> <td>    0.001</td> <td>-1715.538</td> <td> 0.000</td> <td>   -1.001</td> <td>   -0.999</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>         -56.3260</td> <td>          +0.0000j</td> <td>          56.3260</td> <td>           0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.0000</td> <td>          +0.0000j</td> <td>           1.0000</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                             ARIMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:        D2.market_value   No. Observations:                 5019\n",
              "Model:                 ARIMA(1, 2, 1)   Log Likelihood              -27614.159\n",
              "Method:                       css-mle   S.D. of innovations             59.272\n",
              "Date:                Mon, 16 Aug 2021   AIC                          55236.317\n",
              "Time:                        06:16:50   BIC                          55262.401\n",
              "Sample:                    01-11-1994   HQIC                         55245.458\n",
              "                         - 04-05-2013                                         \n",
              "=========================================================================================\n",
              "                            coef    std err          z      P>|z|      [0.025      0.975]\n",
              "-----------------------------------------------------------------------------------------\n",
              "const                    -0.0001      0.001     -0.198      0.843      -0.001       0.001\n",
              "ar.L1.D2.market_value    -0.0178      0.014     -1.258      0.209      -0.045       0.010\n",
              "ma.L1.D2.market_value    -1.0000      0.001  -1715.538      0.000      -1.001      -0.999\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1          -56.3260           +0.0000j           56.3260            0.5000\n",
              "MA.1            1.0000           +0.0000j            1.0000            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 289
        },
        "id": "8SrW8YY6mGEU",
        "outputId": "b91aee26-63d6-4703-e3cf-44f5ec47807f"
      },
      "source": [
        "df['res_ar_1_i_2_ma_1'] = results_ar_1_i_2_ma_1.resid.iloc[:]\n",
        "sgt.plot_acf(df.res_ar_1_i_2_ma_1[2:], zero = False, lags = 40)\n",
        "plt.title(\"ACF Of Residuals for ARIMA(1,2,1)\",size=20)\n",
        "plt.show()"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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p6eksXryYDRs2MHv2bObNm2eaLy8vD4DvvvuO7777rsr1VTzRvvXWW3zwwQekpKSYEky9evUYOHAgzz//fLXtxwsKCgCqPNE5q+9Bfn4+I0eO5Ny5c6YK9KCgILRaLfn5+axYsYKSkhKr65k8eTKNGjXis88+45NPPuHjjz9GpVLRo0cPnnvuOTp16uRQnAUFBQQFBVmsUNVqtaY6kpvV9MrYeAd+8+/IWKT7yy+/cPjwYYufa9q0aUyfPt10lbp8+XI++eQTZsyYwQcffFDjer/Y2FjefPNNkpOTCQ8PR1EUszoyS/R6PatWrUKtVhMbG2s2zVistm3bNrO6EMBUqX39+nWLFdy15cyZM0ycOJErV67w5ptv8te//tVl2za29LTl897yySI3N9fU4ukf//gH//jHPyzOl5SUZEoWxjLUffv2odfra1xvUVPdunVj9erV7N69m6eeeqraeY0tiP70pz85PQ6NRkPr1q1ZtGgRGRkZfPHFF/Tv3990sBqvCF966SWLfT0s8fPzY/r06UyfPp2srCx++OEH1qxZw7p168jIyOCzzz6rclnj9iydAIEq27WrVCpKS0stTrPU3jw5OZlz586ZTnAV/fTTT6xYsaLKGG82fPhwhg8fTn5+Pj/99BObN29m1apVPPzww2zcuNGhu4yGDRty5coVSktLK90Vl5WVcfnyZYvlzJZa9lnz66+/cujQIQDi4+OrnC8pKanaJKhWq9HpdLz88stcuHCB1NRUPv30U5uPn5uFhISYmsgGBARw55130r59+2qX2bZtm+nOsG/fvlXOt2rVKv7+97+bXhsvUvLy8lx2d3Hq1CkmTZpEXl4eb731FlFRUS7ZrpHxgtCWO9Fbvs5izZo1lJaW0qFDB0aOHGnxX0hICLt37yY9PR0oL864/fbbyc7Ottqk0GAwVHkiqqmYmBgCAwM5dOhQtVfs3333HYcOHSI4ONhqGa0j1Go1L730ElDeSkiv1wOYKnj3799fo/XqdDqGDRvG8uXLadWqFQcOHKj2drdNmzbUr1+fY8eOme4yKqqq7XhQUBA5OTkWv6cjR45Ueu+3334DYMCAAZWm/fDDD1XGV53AwED+8pe/8OqrrxIXF0deXl6N12UUGRmJwWCwuP9/+OEH9Ho9d9xxh0PbMDLeVfTs2bPK35Gfnx8pKSlcvXrVpnUmJCTg6+vLsmXLTE2/a2LUqFGUlJSQm5trU8W2sR6nX79+Fj+H8c7piy++oOJTpY39JozFqrXt+PHjTJgwgStXrrB06VKXJwoov6sJDg62qf70lk8WxoPcWIRi6V98fDyKophaGqjVaubOnYtWq+XVV1/lyy+/xNKjyE+ePMmDDz7o9OKqgIAAU8/yp59+2tQKo6Iff/zR1JzthRdesLsNtb26dOlCv379OH36NGvXrgXKK5W7d+/O5s2bTfvuZsePHzfdCeTm5nL8+PFK8xQVFVFUVIRWq6223sjHx4ehQ4dy9erVSnUkhw8fZv369RaX69SpE2VlZZUS/+rVq/nxxx8rzW8cfuLm5HP06FHee++9KuO72Z49eyweN8a6HEeLMu6//34AFi1aRHFxsen94uJiU5NZa02/bXHt2jXWr1+PRqPhjTfeqPJ3NGDAAIqKivjqq69sWm94eDijR48mLy/P5l7Cltx111288847LFu2rFJDi5tlZWWxc+dOgoKCWLx4scXPMX/+fLp160Z6erpZ3x9j3dDBgwdrHOvNjP2ibj42jx07xsSJE7l69SrvvPNOpY6Hlhj7DDlrbLT09HQuXbpEr169bLobvaWLofbu3UtaWhrt27evdnyTkSNH8u6777Jq1SqmT5+OVqulZ8+eLFmyhOeee47nnnuOd955h169etGoUSMKCws5cuQIP//8M/Xr16+V8suRI0dSUFDAv/71L8aNG0fPnj3p0KEDKpWKX375hb1796JWq3nxxRcr9d6uLU888QTbt29n2bJlDB06FF9fXxYtWsSkSZN46aWX+OSTT+jSpQsNGzYkOzubEydOcOLECRITEwkNDeX8+fMMHz6c9u3bExERgU6no7CwkO3bt3Px4kUmTJhgNek99dRTfP/993z88cccOXLE1M9iw4YN9O3bl61bt1ZaZsKECaxevZrZs2fz/fffo9PpOHbsGAcPHjRVuFcUGxvL8uXLee2119i7dy+tWrXit99+Y/v27URHR9s8gNy0adPw9/ena9euNG/eHEVR2L9/P4cPH6ZDhw42NY2uztChQ/nmm2/YuHEjgwcPJioqytTP4ty5c9x3330MGzbMoW1A+bAr+fn59OvXr9oOqKNGjWLdunUkJiZarTcwevTRR/niiy/473//y/jx42tULKdSqWwux//iiy/Q6/UMGzas2krwUaNGceDAARITE039d+666y4CAwPZtWuXxeLhU6dO8cEHH5i9l5+fbxqjCuC5554z+4zGjpMVi7qvXLnC3/72N/Ly8rj77rs5ePCgxQQ1adIkszG5LK3LqGIMxjujN954w9SKbuTIkXTv3t1sGWOphqU7bEtu6WRha0/OFi1acM899/Ddd9+xbds2U7PA/v37s3nzZtNAgqmpqRQWFtKgQQPatGnDE088QXx8fI1althi8uTJ9O3blxUrVrBnzx5TL9lmzZoRHx/PxIkTXTokxh133EF0dDSbNm0iMTGRCRMm0KxZM1atWsWnn37Kpk2bWL9+PXq9nsaNG9OuXTvGjx9vKkM29hXYt28fe/fu5fLlywQHB3P77bfz9NNPW70qhPIy6v/973+8+eabbNu2jSNHjnD77bcze/ZsmjdvbjFZtGvXjo8++oh///vfbNu2DY1GQ/fu3fn888/ZvHlzpWQRFhbGypUreeONNzhw4AC7du2iTZs2zJo1i7vvvtvmZPH000+za9cufvnlF7799lvq1atHeHg4zzzzDA888IBTWt+9+eab9OjRg1WrVpkacrRt25YHH3zQrJmzI2z9HRk7wh05coRjx47ZNA5a06ZNeeCBB/joo494//33zU5qzmYwGEzNja3dccXExDBv3jy2bt1KTk4OoaGh1K9fn7i4OD7++GNOnTpV6bd36dKlSq3xiouLzd6bNm2aWbI4ceIEDRo0MLtzKCgoMNUVfP/996bOgDeLi4szSxYnTpxArVZXGuAQsNhKcNOmTaa/e/bsWSlZrF27lpCQEJuThUqxdB8thBB1UHp6OoMGDWLMmDG8/PLLDq0rPz+fXr16MXnyZJ577jmH1qUoCnfddRd33XUXixcvdmhdUN6gITY2lieffNLmfjC3fJ2FEEI4S8uWLZk4cSJJSUkO11Xu378frVbL5MmTHY7rxIkT5OXlmXqyO+rtt99Gp9Px4IMP2ryM3FkIIUQFhYWF/Pe//+Xuu+926zhRtaW4uJjly5fTo0cPuzoWOy1ZnDlzhoSEBPLy8ggODmbhwoWVBvrS6/W8+uqr7Ny5E5VKxSOPPFKpnPT06dPExcUxduzYap9FIYQQwnWcVgw1a9Ysxo4dS2pqKmPHjmXmzJmV5lm/fj1nz541VaAuWbLE7DGVer2eWbNmuaW9sRBCiKo5JVnk5ORw9OhRhgwZApSPyXT06NFKI29u2LCBUaNGoVarCQkJISoqiq+//to0/f333+fee++1+6laQgghapdTkkVWVhZhYWGm9r8ajYamTZuaRnGsOF94eLjptU6nM4199Ouvv7Jr1y7+9re/OSMkIYQQTuQR/SxKS0v55z//yfz58x0apyknpxCDwbYqmCZNGnLxYuUhJdxN4rKPxGUfics+3h6XWq0iNNS20SGckix0Oh3nz583Dcqn1+u5cOECOp2u0nyZmZmm3tbGO42LFy9y9uxZHnnkEaC8fbKiKBQWFvLKK684I0QhhBAOcEqyCA0NJTIykpSUFGJjY0lJSSEyMrJS1/6YmBiSk5MZMGAAeXl5bNmyhZUrV5rGqTdasmQJRUVF0hpKCCE8hNNaQ82ePZtPP/2UgQMH8umnnzJnzhwApkyZYnpge2xsLC1atGDAgAGMHj2axx9/nJYtWzorBCGEELXEqzrlSZ1F7ZG47CNx2Ufiss8tW2chhPBsBoPCodM55BzMJDTAl85tQlGr7X9Ikqi7JFkI4eUMBoVFiQc5nZlPSakeXx8NbcIDeTq+qyQMYTMZSFAIL3fodA6nM/O5XqpHAa6X6jmdmc+h05YfXyuEJZIshPByZ88XUFKqN3uvpFRP+nnPK4sXnkuShRBe7rawhvj6mHd29fXR0DKsoZsiErciSRZCeLnObUJpEx4IhlJQFOrdqLPo3KZ2ngApvJMkCxcxGBQOnrzEuu/OcPDkJZub+ArhKLVaxdPxXSF7O5orP/NobAep3BZ2k9ZQLiCtUYS7qdUqVFfPoS3Npmu7xu4OR9yC5M7CBaQ1ihDiVifJwgWkNYprSZGfEM4nxVAuYGyNcr1CwpDWKLVDivyEqB1yZ+EC0hrFdaTIT4jaIcnCBSq2RiHnJ2mNUoukyE+I2iHFUC5ibI3C1XPSGqUWSZGfELVD7iyEV5EiPyFqhyQL4VWkyE+I2iHFUC6kUpn//6apFear+sRWzaRa564TbnXP51IUpdI+0WhUqIvOQdE57vyD5SI/WxrTVtysohi/IQXl5uUtvLhWUkaZ3mDDVipw4Mu15RFmCqA3GCitEFel5VTV728VVe07lW079aZ4jPKvXudaaYX9pbIU3I3lKr1t4UNUtc2qv7jfv9ff/4Mqr4iC4tLK67npDwXFps/vrEfNGTRXyS8sKX+hgoD6WrTq2r32l2RB+cn5Wqm+2h+JJYrZEaO68frGyURRMCigGMr/b1AUSsrKfwznLxf/vo4bB5nx+Lxapif/yjXTupUb6/v9oPx9kzem/B6HDfErFZazx8XCEvKvFFuf0cUuFZaSn185ruLr5XUWpzPzzd6v6Y9VqfQFVDVfuaCrZVyxEJfFmZ2m+hVeu16GVq8hLct8n1hazGU9U25sKKi4lCt5Ve+v6o7Z2nzWZ/B1A3l5RbW3gRq6pldMcalUUK9ZIFrf2t2mJAvKd/aF3CKKr5XZvEzFg9fWg7X0RrLIvXKt6pk0GvIKrtsch6v4lRq4XqK3PqOLlZZZjstw40txV8x6g0JZmZ13FrXMeOWs13teJ0VF+f07uxUYDAqns/K5cLmYpo3q00YX6PVFnZIsbii/E7h1DlYhhHsYDApJ20+SlVNEaZkBH60aXag/o+9t59UJQyq46wCDQeFkxhV2H8nmZMYVGf5CCAeczso3JQoov7vNyini9M3Fe15G7iy8XF29ChKitly4XGxKFEalZQYuXC6mXfOgWt22sfgr/2QOgfW1tNEFotG45ncsycLLVXcVVNsHthDeqGmj+vho1WYJw0erpmmj+rW63aou/OL7tavV7RpJMZSXq+4qSAhhvza6QHSh/ij6UhRFMZ202+gCa3W77i7+kmTh5YxXQRW54ipICPDO+jK1WsXoe9tRcm4rZRcOMPSe1i4p1nX3hZ8UQ3k541XQb5mXQa3F10fjkqsgIby5vkytVmEoOIuh4Cztmk9xyTbdVfxlJHcWXs5dV0FCuLvYxNu4q/jLSJJFHWC8Ciq7+BPtmgdJohAu4e5iE29T8cLPcOlHl1/4OS1ZnDlzhvj4eAYOHEh8fDxpaWmV5tHr9cyZM4eoqCiio6NJTk42TVu2bBmDBw9m6NChjBgxgp07dzorNCGEG0h9mfOZir9yfnb5hZ/T6ixmzZrF2LFjiY2N5csvv2TmzJmsWLHCbJ7169dz9uxZNm3aRF5eHsOHD+fuu++mRYsWdO7cmQcffJD69evz66+/Mn78eHbt2oWfn5+zQhRCuJDUl3kXp9xZ5OTkcPToUYYMGQLAkCFDOHr0KLm5uWbzbdiwgVGjRqFWqwkJCSEqKoqvv/4agD59+lC/fvkVR0REBIqikJeX54zwhBBuIPVl3sUpdxZZWVmEhYWh0WgA0Gg0NG3alKysLEJCQszmCw8PN73W6XRkZ2dXWt/atWu57bbbaNasmV1xhIYG2DV/kya/Pz0t52opvn61O+icVlu+f4KD/audz9r02tx2dWojLmewFJczPq+jPG1/uWufqIszoDiD7h2erF+Wt10AAB34SURBVHY+T9tfRlXF5a79efN2VUBQUH2CAurV7nZrde01sG/fPhYvXsyHH35o97I5OYU2t+Nu0qQhFy+WP5dZrVZRkF9MkR2jztZEWVl5MqpuyOPgYP9aGRLZlm1Xp7biclRVcTn6eR1VVVzuHK20rEyPVqtx+T5x53HvqOrictcxdvP3qFJBYH0tJcUldq9LrVbZfJHtlGSh0+k4f/48er0ejUaDXq/nwoUL6HS6SvNlZmbSuXNnoPKdxk8//cSzzz7LO++8Q5s2bZwRmhAew5v7HQjv55Q6i9DQUCIjI0lJSQEgJSWFyMhIsyIogJiYGJKTkzEYDOTm5rJlyxYGDhwIwKFDh3jqqad4++236dChgzPCEsKjSL8DcStzWjHU7NmzSUhI4J133iEwMJCFCxcCMGXKFJ544gk6depEbGwsP//8MwMGDADg8ccfp2XLlgDMmTOHa9euMXPmTNM6X3/9dSIiIpwVohBu5c7RSq2piw/zEfZxWrJo27atWb8Jow8++MD0t0ajYc6cORaXX7VqlbNCEcIjuXu4hqpI8ZiwhfTgFsJF3D1cQ1WkeEzYQpKFEC7iqf0OZFgOYQtJFkK4kCeO0yXDcghbeFw/C1F3SKWqZ3DnsByWHhMqx4BnkmQh3EIqVT2HsXhs3usLUfuFcv+o0S45aXvrMeCtF0GSLIRbyLPBPYs7HubjjceAtyZAkDoL4SZSqSocPQY88ZGt3tyyTO4shFt4ap8D4TqOHAOeegXvyR0vHSV3FsItPLXPgXAdR44BT72C9+aWZZIshFt4ap8D4TqOPCbUU4sxvfkiSJKFcBtP7HMgXKumjwn11Ct4b74IkmQhhLjlePIVvLdeBEmyEELccrz5Ct5TSbIQNeaJTRdF3eGtV/CeSprOegF39Bj11KaLQojaIcniFueuk7Y39r4VQlRNiqFuce5qb+6pTReFELVDksUtzl0nbU9tuiiEqB2SLG5xjp60a1pJ7clNF4UQzid1Frc4R55F4Eh9h7uGtRbCm3ny8OaSLG5xjpy0Ha2kdsew1s7gyT9IUXd5egtDSRZeoKYnbW8eIbMqnv6DFHWXp7cwlDqLOqwuVlJ76milQnh6C0NJFnVYXayk9vQfpKi7PP3iTZJFHVYXx9fx9B+kqLs8/eJNkkUdV9fG1/H0H6Souzz94k2ShahTPP0HKeo2T754k2Qh6hxP/kEK4amclizOnDlDfHw8AwcOJD4+nrS0tErz6PV65syZQ1RUFNHR0SQnJ9s0TQghhHs5rZ/FrFmzGDt2LLGxsXz55ZfMnDmTFStWmM2zfv16zp49y6ZNm8jLy2P48OHcfffdtGjRotppQgjhLW7VTqEqRVEcfmJNTk4OAwcOZO/evWg0GvR6Pb169WLTpk2EhISY5nvkkUcYMWIEMTExAMydO5fw8HAefvjhaqfZat6He7icf92meX18NZSW6MtfqOBaiR693sC1Ej0lZQZ8tWr8fDWoVM77EtPOnACg9e3tq5xHq1VTdlPTTmesu7rpjsRly7LVcXT5msbl6HZrGpcrtl2VtDMnUKlUtGr9hyqng/1xKYpS7e/Glu+iuriq46nfY1XTFEXhYt41Skr1KIAK8PXR0CTYz7TParK//Hw1qGtwrmoUWI+XHrzLpnmdcmeRlZVFWFgYGo0GAI1GQ9OmTcnKyjJLFllZWYSHh5te63Q6srOzrU6zldZHg4+vxub5K85bWmbgfO41iq+XAirUahX1fDQ0C/U3O/BPnTwOQNt2ERbXWd30dn/4Y7XxVLeste1aW3d10x2Jy5FlrS1fm/u6Nr8Ld33m2jxGqlq3oihk5xRX+7upze/CU7/HqqYVXSulpKw8UQAoQEmZnlK9AX8/H6vrrWq6RqtGq7G/VkHrY/v50quG+3j4vkibR01t0qQhFy8WAOUVnqn7zvLF9lOoVOU7XFFAb1D40x+amHW1n7NpEQCjHrrP4nqtTa/OnE2L0Go1Fpd1ZL2Oqi4uW5aFmu+P6pZ1JC5Htl2bcTlyfNmyr4OD/cnLK3JaXCczrrD+YprV34011cVVW8eQO46v3UeyOZ9r3gFUUeAPzYO5p2Mzm9dTcX+pVHBbs0Dq23GhbGRP8ZdTKrh1Oh3nz59Hry8v1tHr9Vy4cAGdTldpvszMTNPrrKwsmjVrZnWaK2RXGALCSHr2OsZgUFA3vA1tkzvlGd1eSnrE2+dW7hTqlGQRGhpKZGQkKSkpAKSkpBAZGWlWBAUQExNDcnIyBoOB3NxctmzZwsCBA61Oc4Vmof637JfoiYwD9vm26I+2aTfW704jaftJSRhe5lY++bmDsVOocZ/dSp1CnVYMNXv2bBISEnjnnXcIDAxk4cKFAEyZMoUnnniCTp06ERsby88//8yAAQMAePzxx2nZsiVAtdNc4Q/Ng9CF+lcajfRW+BI9kXHAPpWmvBzW00bQFM5hPPnJ78Y2xk6ht2JrKKcli7Zt21rsG/HBBx+Y/tZoNMyZM8fi8tVNc4Vb+Uv0RHVx+PO6SH439lOrVbRrHnTL/Q68qoLbUbfql+iJjMUTFROGFE94J/nd1A0y3IeoFbdy2awjjJX66tAudlfqS4MA4cnkzkLUirpYPFGxUh+1lvW702x+Cp8jywrhCnJnIWqNsXjino7N6sSAfRUr9VUqlV1P4XNkWSFcQZKFqJYjxSq1yRPjcqTPgfRXEJ5OiqFElTy1aMRT43KkUl8aBAhPJ3cWokqeWjTiqXE5UqlfVxsEiFuH3FmIKnlqXwlPjatipX7+tTIC/bQ2V+o72iDAVCznF8rJjCte35hAuJ4kC1ElTy0a8dS44PdK/ZoM2FfT/gqeWiwnvIsUQ4kqeWrRiKfG5S6eWiwnvIvcWYgqOVKsUhfjchdPLZYT3kWShaiWI8UqtclT43IHTy6WE95DiqGEuMVJsZxwBbmzEOIWVxeHVhGuJ8lCCC8gI7+K2ibFUEIIIaySZCGEEMIqSRZCCCGskmQhPJI8CEgIzyIV3MLjyPAVQngeubMQHkeGrxDC80iyEB5HHgQkhOeRZCE8jnH4iopk+Aoh3EuShfA4MnyFEJ5HKriFx5HhK4TwPJIshEeS4SuE8CxSDCWEEMIqh5NFcXExM2bMIDo6mpiYGLZt21blvElJSURHRxMVFcXcuXMxGMpbvGzZsoURI0YwZMgQBg8ezIcffuhoWEIIIZzI4WKo5cuXExAQwObNm0lLS2PcuHFs2rSJBg0amM2Xnp7O0qVLWbt2LcHBwUyZMoV169YxfPhwmjRpwn/+8x/CwsIoKChgxIgRdO7cme7duzsanhDCQcbe9Gq/UE5mXJH6ozrK4TuLjRs3Eh8fD0Dr1q3p2LEjO3bsqDRfamoqUVFRhISEoFarGTVqFBs2bACgS5cuhIWFAdCwYUPatm1LRkaGo6EJ4VXcMQRKxd702qbdWL87jaTtJ2X4lTrI4WSRmZlJ8+bNTa91Oh3Z2dmV5svKyiI8PNz0Ojw8nKysrErznTp1ioMHD3LXXXc5GpoQXsNdJ23pTS+MrBZDxcXFkZmZaXHa7t27nRrMhQsXmDp1KrNmzTLdadgjNDTArvmbNGlo+jvnaim+fnqry2i1GgCCg/1rNL2m63Zkvc7izm1XpzbicsZ34cy4fk3LJfvGSRvKe7Rn5xRxIf86f2wdYte67Ikr/2SOxd70+dfKnL7fPe035Qm/ueoY41IBQUH1CQqoV6vbs5os1qxZU+308PBwMjIyCAkpP2CzsrLo1atXpfl0Op1Z0snMzESn05le5+TkMHnyZB5++GEGDRpk8weoKCen0OYrrSZNGnLxYgFQ3kyzIL+YomtlVpcrKytPKHl5RTWabm3dWq3G4rKOrNcZgoP93bbt6tRWXNXtb1u+C2fHdfpcHiU3nbRLygycPpdHs2A/m9djb1yB9bX4aNVmCcNHqybQT+vUz1ddXI7+pqpa1pbfclW/R3eruL9UqvLvqaS4xO71qNUqmy+yHS6GiomJITExEYC0tDQOHz5Mnz59Ks03cOBAtmzZQm5uLgaDgeTkZFNSuHz5MpMnT2bcuHGMGjXK0ZCE8DruGgJFetMLI4dbQz300EMkJCQQHR2NWq1m7ty5BASUZ6rFixfTtGlTHnjgAVq2bMnUqVMZPXo0AL1792bYsGEAvP/++6SlpZGYmGhKPBMnTuT+++93NDwhvILxpJ2VU0RpmcFlJ23pTS+MHE4W/v7+vP322xanPfnkk2avx4wZw5gxYyrN9/zzz/P88887GooQXsudJ23pTS9AhvsQ4pYhJ23XMfUt8W8sfUtukGQhhBAVyJMaLZOxoYQQogLpW2KZJAshhKhAntRomSQLIYSoQJ7UaJkkCyGEqED6llgmFdxCCFFBxWbK+dfKCPTTSmsoJFkIIbyUI0OrG5spe+owN+4gyUII4XWk+avzSbK4oWEDX/zr+1idz1iOGRpcH1BQboxbqCjlf2s15dMDGviWv2dQ0N8Y3NA0L6Y/zKhVKlQVtlFxlvIpxvUrlRe3c6Rqewe2VqnwyB+ZSlW+36xR7PzExjUaV2387uRBQLeGis1fAbPmr9KpsWYkWVB+AghpaNvwvr43TuRNLY70qaKeT/mwxrc1NR/JUVHKT1eKUv6v/PRiftL389Wg1WpobapI+z3J+NUrX2/r8EDTiavidHtUPHGqsC1xBAf5k+df08NFZX92qkbFVQUF+XHFapKvvHFr+6yeb/lnva1ZoGl5gwGWrDqEb8v+oNLy1fdptGoWyLQRnVBVSBiKAoGBfgTc+M7sja3qd2syk7nAhn74+6pBuXEcVFjHzfvE6uoVCxctNrp5mcBAP3xUltfkq1WjAI0b1UepEGR132HByUsWm78WFJcQfOO3brywC25Y7/eLgQr7RAH8/bSU+ftWiNt8o5ViuCk+ey9SbOXrozadE1QqFTZcLzlMksUNtp5wf7+TsDjVdDBXNVS6Cip8saoK/y2nVqvQmE48KrjpL63ZVazrrmgD/H0pvnrdZduzVWCDelwvsn9oZmuMu7m+7+8n/IMnL/FbdgEqdXlyul5q4LfsAk5mXKFru8Zmy4cG1cdQYn3Ie1dr3Mgfpcz6c1tcSaWCxo0D8K3ixGq8024SZPtQ7He0asSOg5lcL/39s9bz0XBHq1B0oQ1MrwHTa0txhYYGkJNTaPN2XeXmuMovQmv3QViSLISw0dnzBZSUmp9oS0r1pJ8vqJQshO2qvwCzPt2STm1CaRMeyOnMfEpK9fj6aGgTHkinNiGmk+rN/69qu576CFlXxyXJQggb3RbWEF8fjdnVqq+PhpZhDatZSriDWq3i6fiuHDqdQ/r5AlqGNaRzm1CpX3KAJAshbNS5iqvVzm1C3R2asECtVtG1XWO563MSSRZC2EiuVkVdJslCCDvI1aqoq2RsKCGEEFZJsvAQBoOC0qAFZUGdOHjykse2wBBC1E2SLDyAwaCwKPEgNLsXfVAX3vvyFxYlHpSEIYTwGJIsPMCh0zmczswHtQ+oVFwv1XM6M59Dp3PcHZoQQgCSLDxCdZ29hBDCE0iy8ADGzl4VSWcvIYQnkWThAYydver5aFBRPmaNdPYSQngS6WfhASp29sotLCEkwFc6ewnB760EqRfKwZOX5HfhRpIsPISxs1eTJg25eFHqKoSo2EoQlZb3vvyFNuGBPB3fVRKGG0gxlBDCI0krQc8iyUII4ZGklaBncThZFBcXM2PGDKKjo4mJiWHbtm1VzpuUlER0dDRRUVHMnTsXg8H8SVbXr19n8ODBjBgxwtGwhBC3uNpsJWisC1FCusiICTZyOFksX76cgIAANm/ezLvvvsvLL7/M1atXK82Xnp7O0qVLSUxMZNOmTfz222+sW7fObJ5///vfdOnSxdGQvI4c2KIuqq1WgmZ1ISF3yogJNnI4WWzcuJH4+HgAWrduTceOHdmxY0el+VJTU4mKiiIkJAS1Ws2oUaPYsGGDafr+/ftJS0sjNjbW0ZC8ihzYoq4ythJ8NLYDw/vczqOxHZxSuS11ITXjcLLIzMykefPmptc6nY7s7OxK82VlZREeHm56HR4eTlZWFgBFRUW89tprzJkzx9FwvI4c2KIuM7YSHNr7drq2a+yUVlBSF1IzVpvOxsXFkZmZaXHa7t27nRLE66+/ztixYwkLCyMtLa3G6wkNDbBr/iZN7C/79PXVVrusten2xpVzMNPigZ1bWOLQNhyNy5M4Oy69QUET1ArFN4QzF6/S7Y9haGpwkqor+8tZXBVXp/ZN+XrvWa6V/P67queroWP7phZjqOv7y8hqslizZk2108PDw8nIyCAkJAQov4Po1atXpfl0Op1Z0snMzESn0wFw4MABduzYwTvvvMP169e5cuUKQ4cOZf369XZ9mJycQpuLZ2ran6GkpAygymWtTbc3rtAAX4vPfQ4J8HVpfwxP7f/h7LiMxX5ljfuASsvrK/bXqG1/XdlfzuLKuFqF+nO7zvzxuLfrAmkV6l8pBm/fX2q1yuaLbIc75cXExJCYmEinTp1IS0vj8OHDLFq0qNJ8AwcOZNy4cUybNo3g4GCSk5MZMmQIgFlS2Lt3LwsXLmT16tWOhuYV5LnPrmVW7AdmxX7ydDzvII/HrRmHk8VDDz1EQkIC0dHRqNVq5s6dS0BAeaZavHgxTZs25YEHHqBly5ZMnTqV0aNHA9C7d2+GDRvm6Oa9nhzYrlVdebYkC+8hj8e1n8PJwt/fn7ffftvitCeffNLs9ZgxYxgzZky16+vVq5fcVdxEDmzXMbbtv7nYT0YAFnWd9OAWogIZAVgIy2QgQSEqkGI/ISyTZCHETaTYT4jKpBhKCCGEVZIshBBCWCXJQgghhFWSLIQQQlglyUIIIYRVkiyEEEJYJclCCCGEVZIshBBCWCXJQgghhFWSLOwgz8IWQtRVkixsJM/CFkLUZZIsbCTPwhZC1GWSLGwkD3kXQtRlkixsZHwoTkXyUBwhRF0hycJG8lAcIURdJs+zsJE8FEcIUZdJsrCDPBRHCFFXSTGUEEIIqyRZCCGEsEqShRBCCKskWQghhLBKkoUQQgirJFkIIYSwSpKFEEIIqyRZCCGEsMrhZFFcXMyMGTOIjo4mJiaGbdu2VTlvUlIS0dHRREVFMXfuXAwGg2nasWPHGDduHPfddx/33Xcf3377raOhCSGEcBKHe3AvX76cgIAANm/eTFpaGuPGjWPTpk00aNDAbL709HSWLl3K2rVrCQ4OZsqUKaxbt47hw4dTVFTEtGnTWLRoEV27dqWsrIyCAhnNVQghPIXDdxYbN24kPj4egNatW9OxY0d27NhRab7U1FSioqIICQlBrVYzatQoNmzYAEBKSgrdunWja9euAGi1Who1auRoaEIIIZzE4TuLzMxMmjdvbnqt0+nIzs6uNF9WVhbh4eGm1+Hh4WRlZQFw8uRJtFotU6ZM4cKFC3To0IHnn3+eoKAgR8MTQgjhBFaTRVxcHJmZmRan7d692ylBGAwG9uzZw+eff07jxo2ZP38+CxYsYP78+XatJzQ0wK75mzRx/rMofH21Dq+7NuJyBonLPhKXfSQu+7g6LqvJYs2aNdVODw8PJyMjg5CQEKD8DqJXr16V5tPpdGZJJzMzE51OZ5rWq1cvmjZtCsDQoUN58cUXbf8UN+TkFNr8TOwmTRpy8aLz60VKSsoAarzu2orLURKXfSQu+0hc9nFWXGq1yuaLbIfrLGJiYkhMTAQgLS2Nw4cP06dPn0rzDRw4kC1btpCbm4vBYCA5OZlBgwYBMGjQIA4dOkRhYSEAO3bsICIiwtHQhBBCOInDdRYPPfQQCQkJREdHo1armTt3LgEB5Zlq8eLFNG3alAceeICWLVsydepURo8eDUDv3r0ZNmwYUH53MmXKFMaMGYNKpaJFixa88sorjoYmhBDCSVSKothWbnML8IRiqIcemgDA8uWf1Gh5b7/tdTaJyz4Sl328PS6XFkMJIYTwfpIshBBCWCXJQgghhFWSLIQQQlglyUIIIYRVkiyEEEJYJclCCCGEVZIshBBCWCXJQgghhFWSLIQQQlglyUIIIYRVkiyEEEJYJclCCCGEVZIsnMhgUFAatEAJ6cLBk5dsHgFXCCE8nSQLJzEYFBYlHoRm90LInbz35S8sSjwoCUMI4RUkWTjJodM5nM7MB7UPqFRcL9VzOjOfQ6dz3B2aEEI4TJKFk5w9X0BJqd7svZJSPennPe/BKUIIYS9JFk5yW1hDfH00Zu/5+mhoGdbQTREJIYTzSLJwks5tQmkTHkg9Hw0qoJ6PhjbhgXRuE+ru0IQQwmFadwfgLdRqFU/Hd+XQ6RzSzxfQMqwhnduEolar3B2aEEI4TJKFE6nVKrq2a0zXdo3dHYoQQjiVFEMJIYSwSpKFEEIIqyRZCCGEsEqShRBCCKu8qoLb3pZHntpSSeKyj8RlH4nLPt4clz3rUCmKIoMXCSGEqJYUQwkhhLBKkoUQQgirJFkIIYSwSpKFEEIIqyRZCCGEsEqShRBCCKskWQghhLBKkoUQQgirJFkIIYSwyquG+7DFmTNnSEhIIC8vj+DgYBYuXEjr1q3dHRb9+/fH19eXevXqAfDMM8/Qp08fl8excOFCUlNTycjIYP369bRv3x5w/36rKi5377fLly/z3HPPcfbsWXx9fWnVqhVz584lJCSEgwcPMnPmTK5fv07z5s3517/+RWioa56cWF1cERERtG/fHrW6/Frx9ddfJyIiwiVxAUydOpVz586hVqvx9/fnn//8J5GRkW4/xqqKy93HmNHSpUtZsmSJ6fh3+fGl1DETJkxQ1q5dqyiKoqxdu1aZMGGCmyMq169fP+X48ePuDkP54YcflMzMzErxuHu/VRWXu/fb5cuXlT179pheL1iwQHnhhRcUvV6vREVFKT/88IOiKIqybNkyJSEhwe1xKYqitG/fXiksLHRZLDfLz883/b1582Zl+PDhiqK4/xirKi53H2OKoihHjhxRHnroIVMs7ji+6lQxVE5ODkePHmXIkCEADBkyhKNHj5Kbm+vmyDxH9+7d0el0Zu95wn6zFJcnCA4OplevXqbXXbt2JTMzkyNHjlCvXj26d+8OwJgxY/j666/dHpcnaNiwoenvwsJCVCqVRxxjluLyBCUlJcydO5fZs2eb3nPH8VWniqGysrIICwtDo9EAoNFoaNq0KVlZWYSEhLg5uvLbW0VR6NatG//4xz8IDAx0d0iA7DdbGQwG/ve//9G/f3+ysrIIDw83TQsJCcFgMJiKWNwVl9GECRPQ6/X07duX6dOn4+vr69KYXnrpJb777jsUReH//u//POYYuzkuI3ceY4sXL2bYsGG0aNHC9J47jq86dWfhyVauXMm6detYtWoViqIwd+5cd4d0S/Ck/fbKK6/g7+/P+PHj3RaDJTfHtX37dlavXs3KlSs5efIky5Ytc3lM8+bNY/v27Tz11FO8/vrrLt9+VSzF5c5j7KeffuLIkSOMHTvWZdusSp1KFjqdjvPnz6PX6wHQ6/VcuHDBI4o3jDH4+voyduxYfvzxRzdH9DvZb9YtXLiQ3377jbfeegu1Wo1OpzMr9snNzUWtVrv8ruLmuOD3fRYQEMCoUaPceqwNHz6cvXv30qxZM486xoxxXb582a3H2A8//MCpU6f461//Sv/+/cnOzuahhx7it99+c/nxVaeSRWhoKJGRkaSkpACQkpJCZGSk24tSioqKKCgoAEBRFDZs2EBkZKRbY6pI9lv13nzzTY4cOcKyZctMxTkdO3bk2rVr7N+/H4DPP/+cmJgYt8d15coVrl27BkBZWRmpqaku3WdXr14lKyvL9Hrr1q0EBQW5/RirKq569eq59Rh75JFH2LVrF1u3bmXr1q00a9aM5cuX8/DDD7v8+KpzDz86deoUCQkJ5OfnExgYyMKFC2nTpo1bY0pPT2f69Ono9XoMBgNt27bl5ZdfpmnTpi6P5dVXX2XTpk1cunSJRo0aERwczFdffeX2/WYprnfffdft++3//b//x5AhQ2jdujV+fn4AtGjRgmXLlvHjjz8ya9Yss6aNjRs3dmtcDz/8MDNnzkSlUlFWVsadd97Jiy++SIMGDVwS16VLl5g6dSrFxcWo1WqCgoJ4/vnn6dChg1uPsariCgwMdPsxVlH//v159913ad++vcuPrzqXLIQQQtivThVDCSGEqBlJFkIIIaySZCGEEMIqSRZCCCGskmQhhBDCKkkWQgghrJJkIYQQwipJFkIIIaz6/7N2P7UIAvJFAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "awTBHn1_m1RX"
      },
      "source": [
        "### 11. ARIMAX Approach"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 358
        },
        "id": "TCef0Q77myKG",
        "outputId": "a0ebc73e-6a7c-407c-dfee-079ce7da8e9d"
      },
      "source": [
        "model_ar_1_i_1_ma_1_Xspx = ARIMA(df.market_value, exog = df.spx, order=(1,1,1))\n",
        "results_ar_1_i_1_ma_1_Xspx = model_ar_1_i_1_ma_1_Xspx.fit()\n",
        "results_ar_1_i_1_ma_1_Xspx.summary()"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARIMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>  <td>D.market_value</td>  <th>  No. Observations:  </th>    <td>5020</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>          <td>ARIMA(1, 1, 1)</td>  <th>  Log Likelihood     </th> <td>-27603.556</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>59.132</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Mon, 16 Aug 2021</td> <th>  AIC                </th>  <td>55217.112</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>06:17:25</td>     <th>  BIC                </th>  <td>55249.718</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-10-1994</td>    <th>  HQIC               </th>  <td>55228.538</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 04-05-2013</td>   <th>                     </th>      <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "            <td></td>              <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>                <td>   -0.5842</td> <td>    2.655</td> <td>   -0.220</td> <td> 0.826</td> <td>   -5.789</td> <td>    4.620</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>spx</th>                  <td>    0.0011</td> <td>    0.002</td> <td>    0.450</td> <td> 0.653</td> <td>   -0.004</td> <td>    0.006</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.D.market_value</th> <td>    0.7456</td> <td>    0.070</td> <td>   10.578</td> <td> 0.000</td> <td>    0.607</td> <td>    0.884</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.D.market_value</th> <td>   -0.7917</td> <td>    0.065</td> <td>  -12.274</td> <td> 0.000</td> <td>   -0.918</td> <td>   -0.665</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.3412</td> <td>          +0.0000j</td> <td>           1.3412</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.2632</td> <td>          +0.0000j</td> <td>           1.2632</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                             ARIMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:         D.market_value   No. Observations:                 5020\n",
              "Model:                 ARIMA(1, 1, 1)   Log Likelihood              -27603.556\n",
              "Method:                       css-mle   S.D. of innovations             59.132\n",
              "Date:                Mon, 16 Aug 2021   AIC                          55217.112\n",
              "Time:                        06:17:25   BIC                          55249.718\n",
              "Sample:                    01-10-1994   HQIC                         55228.538\n",
              "                         - 04-05-2013                                         \n",
              "========================================================================================\n",
              "                           coef    std err          z      P>|z|      [0.025      0.975]\n",
              "----------------------------------------------------------------------------------------\n",
              "const                   -0.5842      2.655     -0.220      0.826      -5.789       4.620\n",
              "spx                      0.0011      0.002      0.450      0.653      -0.004       0.006\n",
              "ar.L1.D.market_value     0.7456      0.070     10.578      0.000       0.607       0.884\n",
              "ma.L1.D.market_value    -0.7917      0.065    -12.274      0.000      -0.918      -0.665\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.3412           +0.0000j            1.3412            0.0000\n",
              "MA.1            1.2632           +0.0000j            1.2632            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fYgOCzgOm4f4"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}