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binary-Q1Uni-GARCH.Rmd
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binary-Q1Uni-GARCH.Rmd
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---
title: "<img src='www/binary-logo-resize.jpg' width='240'>"
subtitle: "[binary.com](https://github.com/englianhu/binary.com-interview-question) Interview Question I - Comparison of Univariate GARCH Models"
author: "[®γσ, Lian Hu](https://englianhu.github.io/) <img src='www/ENG.jpg' width='24'> <img src='www/RYO.jpg' width='24'>®"
date: "`r lubridate::today('Asia/Tokyo')`"
output:
html_document:
number_sections: yes
toc: yes
toc_depth: 4
toc_float:
collapsed: yes
smooth_scroll: yes
---
```{r setup, include=FALSE}
suppressPackageStartupMessages(library('BBmisc'))
#'@ suppressPackageStartupMessages(library('rmsfuns'))
pkgs <- c('knitr', 'kableExtra', 'tint', 'devtools', 'lubridate', 'data.table', 'quantmod', 'tidyquant', 'plyr', 'stringr', 'magrittr', 'dplyr', 'tidyverse', 'rlist', 'memoise', 'htmltools', 'highcharter', 'formattable', 'DT', 'rugarch', 'rmgarch', 'forecast')
suppressAll(lib(pkgs))
#'@ load_pkg(pkgs)
funs <- c('uv_fx.R', 'opt_arma.R', 'filterFX.R', 'filter_spec.R', 'task_progress.R', 'read_umodels.R')
l_ply(funs, function(x) source(paste0('./function/', x)))
options(warn = -1)
rm(pkgs)
```
# Introduction
There are quite some papers study on the GARCH models.
- **EGARCH, GKR-GARCH, TGARCH, AVGARCH, NGARCH, IGARCH and APARCH Models for Pathogens at Marine Recreational Sites**
- **Predictive Accuracy of GARCH, GJR and EGARCH Models Select Exchange Rates Application**
From previous papers, I tried to apply couple models for FOREX price forecasting and eventually got to know *Fractional Intergrated GJR-GARCH* is the best fit model as we can refer to **GARCH模型中的ARIMA(p,d,q)参数最优化**^[Kindly refer to paper in [Reference]]. Due to I simulate whole dataset to get the result in menmtioned paper is time consuming, I tried to apply `dccroll()` to know the mse by resampling but not only based on single `AIC`^[Only the `solver=solnp` stable but the other solvers not stable, the fluctuation of AIC value is quite high.]. I parse my `mv_fx()` function^[Due to some errors] and tested the **Binary-Q1 - Multivariate GARCH Models** and some additive parameters might probably need to be adjusted in the arguments of the function. [Arma Part Overfitting in Arma Garch Model fitting via fGarch Package](https://stackoverflow.com/questions/36312065/arma-part-overfitting-in-arma-garch-model-fitting-via-fgarch-package) is a similar study for models comparison in GARCH.
I try to use 3 methods to compare the GARCH models.
- The default setting is `forecast.length = 500, refit.every = 25, refit.window = 'recursive'`: refit couple times in order to make sure the stability of the prediction model.
- Set `n.start = ns`, `forecast.length = nrow(x) - ns`, `refit.every = 1`, `refit.window = 'moving'`: refit once only with moving to know the prediction accuracy of the Markov model.
- Similar with Markov model above, but just seperates to `ugarchfit()` and `ugarchforecast()` and save every single observation. It will be easy to find the origin of error and rerun that particular data prediction.
Besides using the `ugarchroll()`, all models in this paper are Fractional Intergrated model which optimised the arfima `q` and also adjusted arma order `p` and `q`. **AMATH546 - ECON589 HW3** also teach the use of `ugarchroll()`.
```{r dcc, eval=FALSE}
## --- eval=FALSE, not run but display chunk ---
mv_fx <- function(...) {
...
mod = dccroll(dccSpec, data = mbase, solver = .solver,
forecast.length = 50, cluster = cl)
cat('step 1/1 dccroll done!\n')
...
}
cl = makePSOCKcluster(ncol(mbase))
## Workable
test_roll <- dccroll(dccspec(
multispec(c(ugarchspec(), ugarchspec(), ugarchspec(),
ugarchspec(), ugarchspec(), ugarchspec(),
ugarchspec())), distribution = 'mvt'),
data = mbase, cluster = cl)
## Not workable
test_roll2 <- dccroll(dccspec(
multispec(c(
uspec1 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec2 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec3 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec4 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec5 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec6 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec7 = ugarchspec(variance.model = list(model = 'gjrGARCH'))
))), data = mbase, cluster = cl)
#Error in checkForRemoteErrors(val) :
# one node produced an error: infinite or missing values in 'x'
## Workable
test_roll3 <- dccroll(dccspec(
multispec(c(
uspec1 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec2 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec3 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec4 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec5 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec6 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec7 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm')
)), distribution = 'mvt'), data = mbase, cluster = cl)
## Not workable
test_roll4 <- dccroll(dccspec(
multispec(c(
uspec1 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec2 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec3 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec4 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec5 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec6 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec7 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm')
)), distribution = 'mvt'), data = mbase, cluster = cl)
#Error in checkForRemoteErrors(val) :
# one node produced an error: infinite or missing values in 'x'
```
**Binary-Q1**^[Kindly refer to paper in [Reference]] compares all possible GARCH models in `rugarch` package while the result is in ROI (Return on Investment), due to the paper **Binary-Q1 - Tick-Data-HiLo For Daily Trading <span style='color:red'>(Blooper)</span>** found that the betting strategy is not workable in real-life. Therefore I try to compare again the GARCH models as well as suite for multivariate GARCH models.
Due to the multivartiate models will not coped with every univariate models. Here I tried to compare the accuracy of forecasting by univariate GARCH models and later will compare with the multivariate models.
# Data
## Read Data
Similar with **GARCH模型中的ARIMA(p,d,q)参数最优化**, I use the dataset from **Binary-Q1 (Extention)**^[Kindly refer to paper in [Reference]] to ease the study.
```{r read-data, warning=FALSE}
cr_code <- c('AUDUSD=X', 'EURUSD=X', 'GBPUSD=X', 'CHF=X', 'CAD=X',
'CNY=X', 'JPY=X')
#'@ names(cr_code) <- c('AUDUSD', 'EURUSD', 'GBPUSD', 'USDCHF', 'USDCAD',
#'@ 'USDCNY', 'USDJPY')
names(cr_code) <- c('USDAUD', 'USDEUR', 'USDGBP', 'USDCHF', 'USDCAD', 'USDCNY', 'USDJPY')
## Read presaved Yahoo data.
mbase <- sapply(names(cr_code), function(x) readRDS(paste0('./data/', x, '.rds')) %>% na.omit)
price_type <- c('Op', 'Hi', 'Lo', 'Cl')
gmds <- c('sGARCH', 'fGARCH.GARCH', 'fGARCH.TGARCH', 'fGARCH.AVGARCH', 'fGARCH.NGARCH', 'fGARCH.NAGARCH', 'fGARCH.APARCH', 'fGARCH.GJRGARCH', 'fGARCH.ALLGARCH', 'eGARCH', 'gjrGARCH', 'apARCH', 'iGARCH', 'csGARCH')
timeID <- llply(mbase, function(x) as.character(index(x))) %>%
unlist %>% unique %>% as.Date %>% sort
timeID <- c(timeID, xts::last(timeID) + days(1)) #the last date + 1 in order to predict the next day of last date to make whole dataset completed.
timeID0 <- ymd('2013-01-01')
timeID <- timeID[timeID >= timeID0]
.cl = FALSE
```
# Testing Prediction Result
All my previous papers applied Markov theory which is $p(x_{n}|x_{n-1}...x_{1})$, here I try to test if the model provides same result. Here I iteration 100 times.
```{r em, eval=FALSE}
## ================ eval=FALSE ====================
## sample data.
x <- mbase[['USDJPY']] %>% Cl
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'sGARCH', garchOrder = c(1, 1),
submodel = NULL, external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
fit <- ugarchfit(spec, x, solver = 'hybrid')
## Execute 1 times.
fc1 = ugarchforecast(fit, n.ahead = 1)
## Execute 100 times to know if the coffecient value is applied ML method.
fc2 = replicate(100, ugarchforecast(fit, n.ahead = 1))
## retrieve the series and sigma values.
fc1 <- cbind(attributes(fc1)$`forecast`$seriesFor, attributes(fc1)$`forecast`$sigmaFor)
fc2 <- llply(fc2, function(x) cbind(attributes(x)$`forecast`$seriesFor, attributes(x)$`forecast`$sigmaFor)) %>% do.call('rbind', .)
fc2 %<>% unique
#> rbind(fc1, fc2)
# 2017-08-30 2017-08-30
#T+1 110.4566 0.6523954
#T+1 110.4566 0.6523954
#> fc1 == fc2
# 2017-08-30 2017-08-30
#T+1 TRUE TRUE
rm(x)
```
From above test, we know that the prediction price is exactly same upon testing 100 times.
# GARCH Models
## sGARCH
### Method 1 : Resampling
Below is the backtest simulation. The default setting is `forecast.length = 500, refit.every = 25, refit.window = 'recursive'` which only apply Monte Carlo method to resampling the model.
```{r msesGARCH}
if (!file.exists('data/fx/mse.sGARCH.rds')) {
mse.sGARCH <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'sGARCH', garchOrder = c(1, 1),
submodel = NULL, external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
roll <- ugarchroll(spec, data = x, refit.window = 'recursive',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
#'@ names(mse.sGARCH)[2] <- 'MSE'
mse.sGARCH %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.sGARCH, 'data/fx/mse.sGARCH.rds')
} else {
mse.sGARCH <- readRDS('data/fx/mse.sGARCH.rds')
}
mse.sGARCH %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate sGARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
```
*Table 3.1.1A : MSE of basket currencies.*
### Method 2 : Markov Chain
By refer to below article, I use `ugarchroll()` which is a wrapper for `ugarchfit()` and `ugarchforecast()` which will made the thing use :
- [estimation difference between ugarchroll and ugarchfit](http://r.789695.n4.nabble.com/estimation-difference-between-ugarchroll-and-ugarchfit-td4631122.html)
- [Window size in ugarchroll of rugarch package?](http://r.789695.n4.nabble.com/Window-size-in-ugarchroll-of-rugarch-package-td4669366.html)
There has a concern to use it which is once there has an error during the course of simulation will cause whole data gone.^[`tryCatch()` might useful for `llply()` or else we can use `for()` to skip `NULL` or error result. Normally I will add `cat()` upon completion of one prediction to know the progress of whole simulation.] All my previous preditive result based on the Markov Chain theory^[Markov Chain theory explain the statiscal predicton only can predict the next stage based on current stage. For example in soccer In-Play : 1-0 or 0-1 can be predicted during 0-0, the fit for 0-0 will not be usable anymore once there has scored. Similar concept with scoring intensity in **Dixon & Robinson 1997**, the `armaOrder` and `arfima` parameters optimised the preditive accuracy at every single stage.] with statistical modelling and prediction model and saved every single predictive result.
Below is the simulation . `n.start = ns` is the start point of simulation which is `ymd('2013-01-01')`, `forecast.length = nrow(x) - ns` is the length of forecast equal to the length from the n.start until the end of the dataset, `refit.every = 1` means re-estimate the fit value once only where `refit.window = 'moving'` where today's dataset only can predict 1 trading day in advance.
```{r msesGARCH2}
## --- eval=FALSE ---- Due to errors.
if (!file.exists('data/fx/mse.sGARCH2.rds')) {
mse.sGARCH2 <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'sGARCH', garchOrder = c(1, 1),
submodel = NULL, external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
ns <- which(index(x) == timeID0)
n <- nrow(x) - ns
roll <- ugarchroll(spec, data = x, n.start = ns, forecast.length = n,
refit.every = 1, refit.window = 'moving',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
mse.sGARCH2 %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.sGARCH2, 'data/fx/mse.sGARCH2.rds')
} else {
mse.sGARCH2 <- readRDS('data/fx/mse.sGARCH2.rds')
}
if (!is.null(mse.sGARCH2)) {
mse.sGARCH2 %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate sGARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
}
```
*Table 3.1.1B : MSE of basket currencies.*
### Method 3 : Markov Chain 2
Due to I am not statisfy and doubted onto the `AIC` result based on model comparison by using basic model above. Below I compared the Fractional Intergrated model which optimised the arfima `q` and also adjusted arma order `p` and `q` to proof if my previous study^[gjrGARCH model generated highest ROI.] in **Binary.com Interview Q1** is correct.
**Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading <span style='color:red'>(Blooper)</span>** directly use the mentioned gjrGARCH model but add another criteria which is the timing of daily High-Low price based on highest `bid` and lowest `ask` price within a day.
```{r msesGARCH3, eval=FALSE}
## ------------- Simulate uv_fx() ----------------------
## uv_fx just made the model and some argument flexible.
sGARCH <- list()
for (dt in timeID) {
for (i in seq(cr_code)) {
smp <- mbase[[names(cr_code)[i]]]
timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
if (dt %in% timeID2) {
dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
sGARCH[[i]] <- tryCatch({ldply(price_type, function(y) {
df = uv_fx(smp, .model = 'sGARCH', currency = cr_code[i],
price = y, .cluster = .cl)
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC))
names(df)[4] %<>% str_replace_all('1', 'T+1')
df
})}, error = function(e) NULL)
if (!dir.exists(paste0('data/fx/', names(sGARCH[[i]])[3])))
dir.create(paste0('data/fx/', names(sGARCH[[i]])[3]))
saveRDS(sGARCH[[i]], paste0(
'data/fx/', names(sGARCH[[i]])[3], '/sGARCH.',
unique(sGARCH[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', names(sGARCH[[i]])[3], '/sGARCH.',
unique(sGARCH[[i]]$Date), '.rds saved!\n'))
}
}; rm(i)
}
```
## fGARCH
### GARCH
#### Method 1 : Resampling
The default setting is `forecast.length = 500, refit.every = 25, refit.window = 'recursive'`.
```{r msefGARCH-GARCH, echo=FALSE}
if (!file.exists('data/fx/mse.fGARCH.GARCH.rds')) {
mse.fGARCH.GARCH <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'fGARCH', garchOrder = c(1, 1),
submodel = 'GARCH', external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
roll <- ugarchroll(spec, data = x, refit.window = 'recursive',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
#'@ names(mse.fGARCH.GARCH)[2] <- 'MSE'
mse.fGARCH.GARCH %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.fGARCH.GARCH, 'data/fx/mse.fGARCH.GARCH.rds')
} else {
mse.fGARCH.GARCH <- readRDS('data/fx/mse.fGARCH.GARCH.rds')
}
mse.fGARCH.GARCH %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2], na.rm = TRUE))) %>%
kable(caption = 'MSE for Univariate fGARCH-GARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
```
*Table 3.2.1.1A : MSE of basket currencies.*
#### Method 2 : Markov Chain
Set `n.start = ns`, `forecast.length = nrow(x) - ns`, `refit.every = 1`, `refit.window = 'moving'`.
```{r msefGARCH-GARCH2, echo=FALSE}
if (!file.exists('data/fx/mse.fGARCH.GARCH2.rds')) {
mse.fGARCH.GARCH2 <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'fGARCH', garchOrder = c(1, 1),
submodel = 'GARCH', external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
ns <- which(index(x) == timeID0)
n <- nrow(x) - ns
roll <- ugarchroll(spec, data = x, n.start = ns, forecast.length = n,
refit.every = 1, refit.window = 'moving',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
mse.fGARCH.GARCH2 %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.fGARCH.GARCH2, 'data/fx/mse.fGARCH.GARCH2.rds')
} else {
mse.fGARCH.GARCH2 <- readRDS('data/fx/mse.fGARCH.GARCH2.rds')
}
if (!is.null(mse.fGARCH.GARCH2)) {
mse.fGARCH.GARCH2 %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate fGARCH-GARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
}
```
*Table 3.2.1.1B : MSE of basket currencies.*
#### Method 3 : Markov Chain 2
Below I compared the Fractional Intergrated model which optimised the arfima `q` and also adjusted arma order `p` and `q`.
```{r msefGARCH-GARCH3, eval=FALSE, echo=FALSE}
## ------------- Simulate uv_fx() ----------------------
## uv_fx just made the model and some argument flexible.
fGARCH.GARCH <- list()
for (dt in timeID) {
for (i in seq(cr_code)) {
smp <- mbase[[names(cr_code)[i]]]
timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
if (dt %in% timeID2) {
dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
fGARCH.GARCH[[i]] <- tryCatch({ldply(price_type, function(y) {
df = uv_fx(smp, .model = 'fGARCH', .submodel = 'GARCH',
currency = cr_code[i], price = y, .cluster = .cl)
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC))
names(df)[4] %<>% str_replace_all('1', 'T+1')
df
})}, error = function(e) NULL)
if (!dir.exists(paste0('data/fx/', names(fGARCH.GARCH[[i]])[3])))
dir.create(paste0('data/fx/', names(fGARCH.GARCH[[i]])[3]))
saveRDS(fGARCH.GARCH[[i]], paste0(
'data/fx/', names(fGARCH.GARCH[[i]])[3], '/fGARCH.GARCH.',
unique(fGARCH.GARCH[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', names(fGARCH.GARCH[[i]])[3], '/fGARCH.GARCH.',
unique(fGARCH.GARCH[[i]]$Date), '.rds saved!\n'))
}
}; rm(i)
}
```
### TGARCH
#### Method 1 : Resampling
The default setting is `forecast.length = 500, refit.every = 25, refit.window = 'recursive'`.
```{r msefGARCH-TGARCH, echo=FALSE}
if (!file.exists('data/fx/mse.fGARCH.TGARCH.rds')) {
mse.fGARCH.TGARCH <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'fGARCH', garchOrder = c(1, 1),
submodel = 'TGARCH', external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
roll <- ugarchroll(spec, data = x, refit.window = 'recursive',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
#'@ names(mse.fGARCH.TGARCH)[2] <- 'MSE'
mse.fGARCH.TGARCH %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.fGARCH.TGARCH, 'data/fx/mse.fGARCH.TGARCH.rds')
} else {
mse.fGARCH.TGARCH <- readRDS('data/fx/mse.fGARCH.TGARCH.rds')
}
mse.fGARCH.TGARCH %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate fGARCH-TGARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
```
*Table 3.2.2.1A : MSE of basket currencies.*
#### Method 2 : Markov Chain
Set `n.start = ns`, `forecast.length = nrow(x) - ns`, `refit.every = 1`, `refit.window = 'moving'`.
```{r msefGARCH-TGARCH2, echo=FALSE}
if (!file.exists('data/fx/mse.fGARCH.TGARCH2.rds')) {
mse.fGARCH.TGARCH2 <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'fGARCH', garchOrder = c(1, 1),
submodel = 'TGARCH', external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
ns <- which(index(x) == timeID0)
n <- nrow(x) - ns
roll <- ugarchroll(spec, data = x, n.start = ns, forecast.length = n,
refit.every = 1, refit.window = 'moving',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
mse.fGARCH.TGARCH2 %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.fGARCH.TGARCH2, 'data/fx/mse.fGARCH.TGARCH2.rds')
} else {
mse.fGARCH.TGARCH2 <- readRDS('data/fx/mse.fGARCH.TGARCH2.rds')
}
if (!is.null(mse.fGARCH.TGARCH2)) {
mse.fGARCH.TGARCH2 %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate fGARCH-TGARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
}
```
*Table 3.2.2.1B : MSE of basket currencies.*
#### Method 3 : Markov Chain 2
Below I compared the Fractional Intergrated model which optimised the arfima `q` and also adjusted arma order `p` and `q`.
```{r msefGARCH-TGARCH3, eval=FALSE, echo=FALSE}
## ------------- Simulate uv_fx() ----------------------
## uv_fx just made the model and some argument flexible.
fGARCH.TGARCH <- list()
for (dt in timeID) {
for (i in seq(cr_code)) {
smp <- mbase[[names(cr_code)[i]]]
timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
if (dt %in% timeID2) {
dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
fGARCH.TGARCH[[i]] <- tryCatch({ldply(price_type, function(y) {
df = uv_fx(smp, .model = 'fGARCH', .submodel = 'TGARCH',
currency = cr_code[i], price = y, .cluster = .cl)
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC))
names(df)[4] %<>% str_replace_all('1', 'T+1')
df
})}, error = function(e) NULL)
if (!dir.exists(paste0('data/fx/', names(fGARCH.TGARCH[[i]])[3])))
dir.create(paste0('data/fx/', names(fGARCH.TGARCH[[i]])[3]))
saveRDS(fGARCH.TGARCH[[i]], paste0(
'data/fx/', names(fGARCH.TGARCH[[i]])[3], '/fGARCH.TGARCH.',
unique(fGARCH.TGARCH[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', names(fGARCH.TGARCH[[i]])[3], '/fGARCH.TGARCH.',
unique(fGARCH.TGARCH[[i]]$Date), '.rds saved!\n'))
}
}; rm(i)
}
```
### AVGARCH
#### Method 1 : Resampling
The default setting is `forecast.length = 500, refit.every = 25, refit.window = 'recursive'`.
```{r msefGARCH-AVGARCH, echo=FALSE}
if (!file.exists('data/fx/mse.fGARCH.AVGARCH.rds')) {
mse.fGARCH.AVGARCH <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'fGARCH', garchOrder = c(1, 1),
submodel = 'AVGARCH', external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
roll <- ugarchroll(spec, data = x, refit.window = 'recursive',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
#'@ names(mse.fGARCH.AVGARCH)[2] <- 'MSE'
mse.fGARCH.AVGARCH %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.fGARCH.AVGARCH, 'data/fx/mse.fGARCH.AVGARCH.rds')
} else {
mse.fGARCH.AVGARCH <- readRDS('data/fx/mse.fGARCH.AVGARCH.rds')
}
mse.fGARCH.AVGARCH %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate fGARCH-AVGARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
```
*Table 3.2.3.1A : MSE of basket currencies.*
#### Method 2 : Markov Chain
Set `n.start = ns`, `forecast.length = nrow(x) - ns`, `refit.every = 1`, `refit.window = 'moving'`.
```{r msefGARCH-AVGARCH2, echo=FALSE}
if (!file.exists('data/fx/mse.fGARCH.AVGARCH2.rds')) {
mse.fGARCH.AVGARCH2 <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'fGARCH', garchOrder = c(1, 1),
submodel = 'AVGARCH', external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
ns <- which(index(x) == timeID0)
n <- nrow(x) - ns
roll <- ugarchroll(spec, data = x, n.start = ns, forecast.length = n,
refit.every = 1, refit.window = 'moving',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
mse.fGARCH.AVGARCH2 %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.fGARCH.AVGARCH2, 'data/fx/mse.fGARCH.AVGARCH2.rds')
} else {
mse.fGARCH.AVGARCH2 <- readRDS('data/fx/mse.fGARCH.AVGARCH2.rds')
}
if (!is.null(mse.fGARCH.AVGARCH2)) {
mse.fGARCH.AVGARCH2 %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate fGARCH-AVGARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
}
```
*Table 3.2.3.1B : MSE of basket currencies.*
#### Method 3 : Markov Chain 2
Below I compared the Fractional Intergrated model which optimised the arfima `q` and also adjusted arma order `p` and `q`.
```{r msefGARCH-AVGARCH3, eval=FALSE, echo=FALSE}
## ------------- Simulate uv_fx() ----------------------
## uv_fx just made the model and some argument flexible.
fGARCH.AVGARCH <- list()
for (dt in timeID) {
for (i in seq(cr_code)) {
smp <- mbase[[names(cr_code)[i]]]
timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
if (dt %in% timeID2) {
dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
fGARCH.AVGARCH[[i]] <- tryCatch({ldply(price_type, function(y) {
df = uv_fx(smp, .model = 'fGARCH', .submodel = 'AVGARCH',
currency = cr_code[i], price = y, .cluster = .cl)
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC))
names(df)[4] %<>% str_replace_all('1', 'T+1')
df
})}, error = function(e) NULL)
if (!dir.exists(paste0('data/fx/', names(fGARCH.AVGARCH[[i]])[3])))
dir.create(paste0('data/fx/', names(fGARCH.AVGARCH[[i]])[3]))
saveRDS(fGARCH.AVGARCH[[i]], paste0(
'data/fx/', names(fGARCH.AVGARCH[[i]])[3], '/fGARCH.AVGARCH.',
unique(fGARCH.AVGARCH[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', names(fGARCH.AVGARCH[[i]])[3], '/fGARCH.AVGARCH.',
unique(fGARCH.AVGARCH[[i]]$Date), '.rds saved!\n'))
}
}; rm(i)
}
```
### NGARCH
#### Method 1 : Resampling
The default setting is `forecast.length = 500, refit.every = 25, refit.window = 'recursive'`.
```{r msefGARCH-NGARCH, echo=FALSE}
if (!file.exists('data/fx/mse.fGARCH.NGARCH.rds')) {
mse.fGARCH.NGARCH <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'fGARCH', garchOrder = c(1, 1),
submodel = 'NGARCH', external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
roll <- ugarchroll(spec, data = x, refit.window = 'recursive',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
#'@ names(mse.fGARCH.NGARCH)[2] <- 'MSE'
mse.fGARCH.NGARCH %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.fGARCH.NGARCH, 'data/fx/mse.fGARCH.NGARCH.rds')
} else {
mse.fGARCH.NGARCH <- readRDS('data/fx/mse.fGARCH.NGARCH.rds')
}
mse.fGARCH.NGARCH %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate fGARCH-NGARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
```
*Table 3.2.4.1A : MSE of basket currencies.*
#### Method 2 : Markov Chain
Set `n.start = ns`, `forecast.length = nrow(x) - ns`, `refit.every = 1`, `refit.window = 'moving'`.
```{r msefGARCH-NGARCH2, echo=FALSE}
if (!file.exists('data/fx/mse.fGARCH.NGARCH2.rds')) {
mse.fGARCH.NGARCH2 <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'fGARCH', garchOrder = c(1, 1),
submodel = 'NGARCH', external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
ns <- which(index(x) == timeID0)
n <- nrow(x) - ns
roll <- ugarchroll(spec, data = x, n.start = ns, forecast.length = n,
refit.every = 1, refit.window = 'moving',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique