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binary-Q1Multi-GARCH.Rmd
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binary-Q1Multi-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 - Multivariate GARCH Models"
author: "[®γσ, Lian Hu](https://englianhu.github.io/) <img src='www/RYO.jpg' width='24'> <img src='www/RYU.jpg' width='24'> <img src='www/ENG.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
code_folding: hide
---
```{r setup}
suppressPackageStartupMessages(library('BBmisc'))
#'@ suppressPackageStartupMessages(library('rmsfuns'))
pkgs <- c('knitr', 'kableExtra', 'devtools', 'lubridate', 'data.table', 'quantmod', 'qrmtools', 'tidyquant', 'plyr', 'stringr', 'magrittr', 'dplyr', 'tidyverse', 'memoise', 'highcharter', 'formattable', 'DT', 'rugarch', 'ccgarch', 'mgarchBEKK', 'rmgarch')
suppressAll(lib(pkgs))
#'@ load_pkg(pkgs)
funs <- c('calc_fx.R', 'opt_arma.R', 'filterFX.R', 'filter_spec.R', 'mv_fx.R', 'read_umodels.R')
l_ply(funs, function(x) source(paste0('./function/', x)))
options(warn=-1)#, 'scipen'=100, 'digits'=4)
rm(pkgs)
```
# Introduction
From previous papers, I tried to apply few models for FOREX price forecasting and eventually got to know <span style='color:red'>Fractional Intergrated GJR-GARCH</span> is the best fit model as we can refer to <span style='color:goldenrod'>*GARCH模型中的ARIMA(p,d,q)参数最优化*</span>. **The standalone ARFIMAX model and methods** in the [A short introduction to the rugarch package](http://www.unstarched.net/r-examples/rugarch/a-short-introduction-to-the-rugarch-package/) describe the `autoarfima()` function where we can easily get the optimal MA and AR figure.
Today I am zooming into the multivariate GARCH models.
# Data
## Read Data
Similar with <span style='color:goldenrod'>*GARCH模型中的ARIMA(p,d,q)参数最优化*</span>, I use the dataset from [Binary-Q1 (Extention)](http://rpubs.com/englianhu/binary-Q1E).
```{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_types <- c('OHLC', 'HLC', 'HL', 'C')
## all currencies trading day.
timeID <- llply(mbase, function(x) as.character(index(x))) %>%
unlist
timeID %<>% plyr::count()
#timeID %>% dplyr::count(freq)
## A tibble: 4 x 2
# freq n
# <int> <int>
#1 1 1
#2 3 1
#3 6 3
#4 7 1472
timeID %<>% dplyr::filter(freq == 7) %>% .$x %>% 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 %<>% .[. >= timeID0]
.cl = TRUE
```
# Modelling
## Introduce Multivariate Garch Models
Multivariate GARCH models including DCC, GO-GARCH and Copula-GARCH, CCC and BEKK. Paper <span style='color:goldenrod'>*Comparison of Multivariate GARCH Models with Application to Zero-Coupon Bond Volatility*</span> compares DCC and BEKK model on bond market with maturities of 6 months, 1 year and 2 years. The thesis concludes that the fitting performance of the BEKK is better than DCC in their case, the difference might due to the number of the parameters of BEKK model is comparatively more, so that the BEKK has a better capanility in explaning the information hidden in the hostory data. In opposite, the DCC model has an advantage over the BEKK model in the area of forecasting as the DCC model is more parsimonious than BEKK model. From my understanding means that if we compare with deviance or AIC/BIC the DCC will be more accurate. However, this paper will compare as well since forex market is not bond market.
[**R - Time Series** : Comandos R para análises de séries temporais](https://rpubs.com/EconFin/mgarch) is a website to introduce the multivariate GARCH models (in Portuguese language).
<span style='color:goldenrod'>*Currency Hedging Strategies Using Dynamic Multivariate GARCH*</span> compares DCC, BEKK, CCC and VARMA-AGARCH models to examine the conditional volatilities among the spot and two distint futures maturities, namely near-month and next-to-near-month contracts. The estimated conditionl covariances matrices from these models were used to calculate the optimal portfolios weights and optimal hedge ratios.^[Kindly refer to ] The empirical results in the paper reveal that there are not big differences either the near-month or next-to-near-month contract is used for hedge spot position on currencies. They also reveal that hedging ratios are lower for near-month contract when the USD/EUR and USD/JPY exchange rates are anlyzed. This result is explained in terms of the higher correlation between spot prices and the next-to-near-month future prices than that with near-month contract and additionally because of the lower volatility of the long maturity futures. Finally across all currencies and error densities, the CCC and VARMA-AGARCH models provide similar results in terms of hedging ratios, portfolio variance reduction and hedging effectiveness. Some difference might appear when the DCC and BEKK models are used. Below is the table summary of the paper.
```{r, echo=FALSE}
dfm1 <- data_frame(
Model = c('CCC'),
Currency = c('EURS', 'GBPS', 'JPYS'),
AIC = c(2.738605, 2.247209, 2.827915))
dfm2 <- data_frame(
Model = c('VARMA-AGARCH'),
Currency = c('EURS', 'GBPS', 'JPYS'),
AIC = c(2.734926, 2.241061, 2.828964))
dfm3 <- data_frame(
Model = c('DCC'),
Currency = c('EURS', 'GBPS', 'JPYS'),
AIC = c(2.721337, 2.205663, 2.784974))
dfm4 <- data_frame(
Model = c('BEKK'),
Currency = c('EURS', 'GBPS', 'JPYS'),
AIC = c(2.735964, 2.212324, 2.788730))
dfm <- list(dfm1, dfm2, dfm3, dfm4) %>%
bind_rows %>%
mutate_if(is.character, as.factor) %>%
arrange(Currency)
rm(dfm1, dfm2, dfm3, dfm4)
dfm %>%
kable(caption = 'Comparison Summary') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
group_rows('EURS', 1, 4, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('GBPS', 5, 8, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('JPYS', 9, 12, label_row_css = 'background-color: #003399; color: #fff;') %>%
scroll_box(width = '100%', height = '400px')
```
*Table 3.1.1 : comparison of the models.*
Table above shows DCC model is the best fit model.
<span style='color:goldenrod'>*Do We Really Need Both BEKK and DCC - A Tale of Two Multivariate GARCH Models*</span> compares few models and final model should be based on model performance within the appropriate framework in which they are used (such as covariance, correlation forecasting, risk monitoringm or portfolio allocation, to cite the most relevant), the paper concludes that the cDCC (constant DCC) model^[Similar with paper <span style='color:goldenrod'>*Aielli (2010)*</span> who suggest using cDCC model insted of the DCC model of <span style='color:goldenrod'>*Engle (2002)*</span>. Similar with papers <span style='color:goldenrod'>*Engle et al. (2008)*</span> and <span style='color:goldenrod'>*Engle Engle and Kelly (2009)*</span>.] and BEKK model.
<span style='color:goldenrod'>*Forecasting the Daily Dynamic Hedge Ratios by GARCH Models - Evidence from the Agricultural Futures Markets*</span> compares few models which are bivariate GARCH, BEKK GARCH, GARCH-X, BEKK-X, Q-GARCH and GARCH-GJR in agricultural futures markets. The paper reveals that the BEKK model dominates others models for storable wheat and soybean for both forecasting horizons, and the asymmetric GJR andQ-GARCH models does the best forecasting performance for the non-storable products, live cattle and live hogs.
<span style='color:goldenrod'>*Dynamic Portfolio Optimization using Generalized Dynamic Conditional Heteroskedastic Factor Models*</span> studies the portfolio selection problem based on a generalized dynamic factor model (GDFM) with conditional heteroskedasticity in the idiosyncratic components. We propose a Generalized Smooth Transition Conditional Correlation (GSTCC) model for the idiosyncratic components combined with the GDFM. Among all the multivariate GARCH models that the authors propose, the generalized smooth transition conditional correlation provides the best result.
I try to surf over internet and the model has no yet widely use. Here I can only use the CCC, DCC models but the best performance GSTCC is not yet available in r packages. The `cccgarch` has STCC model but there has no examples to use it. I roughly read over the `ccgarch` package and noticed that all parameters required in matrix format which is only suitable for advance user use.
<span style='color:goldenrod'>*Forecasting Conditional Correlation for Exchange Rates using Multivariate GARCH Models with Historical Value-at-Risk Application*</span> compares the VaR for trade in USDSEK in T+1 and T+10 with intraday 30 minutes time interval. When comparing the BEKK and DCC model, the BEKK seems to perform better than the DCC in both forecasting conditional correlation and predicting VaR. On the contrary, the BEKK is much more computationally demanding, which most certainly would be even more noticeable when the number of assets increase.
## Parameter Selection
```{r dcc1, echo=FALSE, eval=FALSE}
## ---------- eval = FALSE --------------------
### ========= using cluster for sampling ===============
fit <- llply(na.omit(Cl(mbase[['USDJPY']])), function(x){
armaOrder = opt_arma(x)
xspec = ugarchspec(
variance.model = list(
model = 'gjrGARCH', 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')
uspec = multispec(replicate(4, xspec))
spec1 = dccspec(uspec = uspec, dccOrder = c(1, 1),
model='aDCC', distribution = 'mvt')
cl = makePSOCKcluster(4)
multf = multifit(uspec, x, cluster = cl)
fit1 = dccfit(spec1, data = x, solver = 'hybrid',
fit.control = list(eval.se = TRUE),
fit = multf, cluster = cl)
return(fit1)
})
```
My initially workable models result.
```{r wdcc-aic}
workable.dcc <- readRDS('data/fx/pt.dcc.rds')
#'@ dcc.AIC <- ldply(workable.dcc, function(x) {
#'@ ldply(x, function(y) {
#'@ list.select(y, AIC) %>%
#'@ data.frame %>% t %>% data.frame %>%
#'@ mutate(includes.Op = c(TRUE, FALSE))
#'@ }) %>% rename(.solver = .id)
#'@ }) %>%
#'@ dplyr::select(.id, .solver, includes.Op, Akaike, Bayes, Shibata, Hannan.Quinn)
dcc.AIC <- ldply(workable.dcc, function(x) {
zz <- ldply(x, function(y) {
zz <- ldply(y, function(z) {
z$AIC %>%
data.frame %>% t %>% data.frame
})
names(zz)[1] <- 'includes.Op'
zz
})
names(zz)[1] <- '.solver'
zz
})
dcc.AIC %>%
arrange(Akaike, Bayes) %>%
kable(caption = 'Akaike Information Criteria') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')
```
*Table 3.2.1.1 : AIC comparison.*
From above table, `r unlist(dcc.AIC$Akaike) %>% .[which.min(.)] %>% names` with `r unlist(dcc.AIC$Akaike) %>% .[which.min(.)]` is the best fitted model.
```{r dcc-llh}
dcc.logLik <- ldply(workable.dcc, function(x) {
zz = ldply(x, function(y) {
zz = ldply(y, function(z) {
attributes(z$fit)$mfit$llh
})
names(zz) <- c('includes.Op', 'log.Likelihood')
zz
})
names(zz)[1] <- '.solver'
zz
})
dcc.logLik %>%
arrange(log.Likelihood) %>%
kable(caption = 'Log-Likelihood') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')
```
*Table 3.2.1.2 : Log-Likelihood comparison.*
### Close Price
```{r bk-dcc, eval=FALSE}
## ------- eval ----------
## Possible multivariate models.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp', 'nlminb', 'lbfgs', 'gosolnp')
## Includes the open price or not.
bk.base <- llply(mbase, Cl)
bk.base %<>% do.call(cbind, .) %>% na.omit
## Statistical modelling
bk.dcc <- llply(md, function(x) {
dm <- llply(sv, function(y) {
fit <- tryCatch(
mv_fx(bk.base, .model = x, .solver = y,
.include.Op = FALSE, .Cl.only = TRUE),
error = function(e) cat(paste0('bk.', x, '.', y, ' error.\n')))
if (!is.null('fit')) {
eval(parse(text = paste0(
"saveRDS(fit, 'data/fx/", paste0('bk.', x, '.', y), ".rds')")))
cat(paste0('bk.', x, '.', y, ' saved.\n'))
}
})
names(dm) <- sv
dm
})
names(bk.dcc) <- md
```
I executed above coding and there are quite some models occured errors. The `FDCC` models do faced error even though change all possible solvers. Below I read presaved data which executed above.
```{r read-bkdcc}
fls <- list.files('data/fx', pattern = '^bk.') %>% str_replace_all('.rds', '')
bk.dcc <- sapply(fls, function(x) readRDS(paste0('data/fx/', x, '.rds'))) %>%
filterNull
```
Here I tried to compare the AIC values. The lowest value will be best fit model.
```{r bkdcc-aic}
##compare AIC values.
dcc.AIC <- sapply(bk.dcc, function(x) data.frame(t(x$AIC))) %>%
t %>% data.frame(.id = rownames(.)) %>%
separate(.id, c('.id', '.model', '.solver')) %>%
dplyr::select(.id, .model, .solver, Akaike, Bayes, Shibata, Hannan.Quinn) %>%
unnest
rownames(dcc.AIC) <- NULL
dcc.AIC %>%
arrange(Akaike, Bayes) %>%
kable(caption = 'Akaike Information Criteria') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%')#, height = '400px')
```
*Table 3.2.3.1 : AIC comparison.*
From above table, `r unlist(dcc.AIC$Akaike) %>% .[which.min(.)] %>% names` with `r unlist(dcc.AIC$Akaike) %>% .[which.min(.)]` is the best fitted model.
After that, look at the log-likehood figure as well to compare the correlation among models. The highest value will be best fit model.
```{r bkdcc-logLik}
##compare AIC values.
dcc.logLik <- sapply(bk.dcc, function(x) attributes(x$fit)$mfit$llh) %>%
t %>% t %>% data.frame(.id = rownames(.)) %>%
separate(.id, c('.id', '.model', '.solver'))
rownames(dcc.logLik) <- NULL
names(dcc.logLik)[1] <- 'log.Likelihood'
dcc.logLik %<>% dplyr::select(.id, .model, .solver, log.Likelihood)
dcc.logLik %>%
arrange(log.Likelihood) %>%
kable(caption = 'Log-Likelihood') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
```
*Table 3.2.3.2 : Log-Likelihood comparison.*
```{r bkdcc-roll}
## Possible multivariate models.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp', 'nlminb', 'lbfgs', 'gosolnp')
## Includes the open price or not.
bk.base <- llply(mbase, Cl)
bk.base %<>% do.call(cbind, .) %>% na.omit
## Statistical modelling
bk.dcc <- llply(md, function(x) {
dm <- llply(sv, function(y) {
fit <- tryCatch(
mv_fx(bk.base, .model = x, .solver = y,
.include.Op = FALSE, .Cl.only = TRUE, .roll = TRUE),
error = function(e) cat(paste0('roll.bk.', x, '.', y, ' error.\n')))
if (!is.null('fit')) {
eval(parse(text = paste0(
"saveRDS(fit, 'data/fx/", paste0('roll.bk.', x, '.', y), ".rds')")))
cat(paste0('roll.bk.', x, '.', y, ' saved.\n'))
}
})
names(dm) <- sv
dm
})
names(bk.dcc) <- md
```
### Hi-Lo Price
#### Single Currency
Multivariate modelling for single currency. Here I tried to seperate to 2 type of forecasting dataset which are `OHLC` and `HLC` to know if includes the open price will be more accurate or not.
```{r pt-dcc, eval=FALSE}
## ------------- eval ---------------
## Possible multivariate models.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp', 'nlminb', 'lbfgs', 'gosolnp')
op <- c(TRUE, FALSE)
## Includes the open price or not.
pt.base <- mbase[['USDJPY']][,1:4]
## Statistical modelling
pt.dcc <- llply(md, function(x) {
dm <- llply(sv, function(y) {
TF <- llply(op, function(z) {
fit <- tryCatch(
mv_fx(pt.base, .model = x, .solver = y,
.include.Op = z, .Cl.only = FALSE),
error = function(e)
cat(paste0('pt.', x, '.', y, '.', z,' error.\n')))
if (!is.null('fit')) {
eval(parse(text = paste0(
"saveRDS(fit, 'data/fx/",
paste0('pt.', x, '.', y, '.', z), ".rds')")))
cat(paste0('pt.', x, '.', y, '.', z, ' saved.\n'))
}
})
names(TF) <- op
TF
})
names(dm) <- sv
dm
})
names(pt.dcc) <- md
```
I executed above coding and there are quite some models occured errors. The `FDCC` models do faced error even though change all possible solvers. Below I read presaved data which executed above.
```{r read-ptdcc}
fls <- list.files('data/fx', pattern = '^pt.[^dcc]') %>% str_replace_all('.rds', '')
pt.dcc <- sapply(fls, function(x) readRDS(paste0('data/fx/', x, '.rds'))) %>%
filterNull
```
Here I tried to compare the AIC values. The lowest value will be best fit model.
```{r ptdcc-aic}
##compare AIC values.
dcc.AIC <- sapply(pt.dcc, function(x) data.frame(t(data.frame(x$AIC)))) %>%
t %>% data.frame(.id = rownames(.)) %>%
separate(.id, c('.id', '.model', '.solver', 'includes.Op')) %>%
dplyr::select(.id, .model, .solver, includes.Op, Akaike, Bayes, Shibata, Hannan.Quinn) %>% unnest
rownames(dcc.AIC) <- NULL
dcc.AIC %>%
arrange(Akaike, Bayes) %>%
kable(caption = 'Akaike Information Criteria') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')
```
*Table 3.2.4.1 : AIC comparison.*
From above table, `r unlist(dcc.AIC$Akaike) %>% .[which.min(.)] %>% names` with `r unlist(dcc.AIC$Akaike) %>% .[which.min(.)]` is the best fitted model. After that, look at the log-likehood figure as well to compare the correlation among models. The highest value will be best fit model.
```{r ptdcc-logLik}
##compare AIC values.
dcc.logLik <- sapply(pt.dcc, function(x) attributes(x$fit)$mfit$llh) %>%
t %>% t %>% data.frame(.id = rownames(.)) %>%
separate(.id, c('.id', '.model', '.solver', 'includes.Op'))
rownames(dcc.logLik) <- NULL
names(dcc.logLik)[1] <- 'log.Likelihood'
dcc.logLik %<>% dplyr::select(.id, .model, .solver, includes.Op, log.Likelihood)
dcc.logLik %>%
arrange(log.Likelihood) %>%
kable(caption = 'Log-Likelihood') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
```
*Table 3.2.4.2 : Log-Likelihood comparison.*
The model `r dcc.logLik %>% dplyr::filter(log.Likelihood == max(log.Likelihood)) %>% unite(.id, .id:includes.Op) %>% .$.id %>% str_replace_all('_', '.')` which highest logLik value `r dcc.logLik$log.Likelihood[which.max(dcc.logLik$log.Likelihood)]` is the best fitted model for correlation.
```{r ptdcc-roll, eval=FALSE}
## ------------- eval ---------------
## Possible multivariate models.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp', 'nlminb', 'lbfgs', 'gosolnp')
op <- c(TRUE, FALSE)
## Includes the open price or not.
pt.base <- mbase[['USDJPY']][,1:4]
## Statistical modelling
pt.dcc <- llply(md, function(x) {
dm <- llply(sv, function(y) {
TF <- llply(op, function(z) {
fit <- tryCatch(
mv_fx(pt.base, .model = x, .solver = y,
.include.Op = z, .Cl.only = FALSE, .roll = TRUE),
error = function(e)
cat(paste0('roll.pt.', x, '.', y, '.', z,' error.\n')))
if (!is.null('fit')) {
eval(parse(text = paste0(
"saveRDS(fit, 'data/fx/",
paste0('roll.pt.', x, '.', y, '.', z), ".rds')")))
cat(paste0('roll.pt.', x, '.', y, '.', z, ' saved.\n'))
}
})
names(TF) <- op
TF
})
names(dm) <- sv
dm
})
names(pt.dcc) <- md
```
#### Currency Basket
Multivariate modelling for a basket of currencies for `Cl` will compares in following section. The `HL` and `HLC` will be in another paper.
### Concludes Parameter Selection
I initially wonder if I need to includes the open price in the models. Therefore I tried to compare above models. However the open price might not in use the my trading strategy. Therefore here I skip it. Here I seperates to 3 selection for trading:
- Hi-Lo
- Hi-Lo-Cl
- Cl
From previous univariate models comparison, gjrGARCH almost be the most accurate across all mentioned currencies. Due to the MSE of USDJPY will be higher than other currency, here I use USDJPY to save the time to compare the models. Above solver shows that the `solnp` and `gosolnp` will be more accurate, here I only use these 2 solvers. I skip the `Open Price` because it will not use in either be punter nor banker.
*Source : [转载]詹姆斯-哈里斯-西蒙斯(James Harris Simons)*
<span style='color:goldenrod'>*[转载]詹姆斯-哈里斯-西蒙斯(James Harris Simons)*</span> describe the open price of future market and the close price of last day was highly related. There will be another research (if any). However I tried to use previous day's price to model in `VAR=TRUE`.
## DCC
### Abtract of DDC
Due to article <span style='color:goldenrod'>*The GARCH DCC Model and 2 Stage DCCMVT Estimation*</span>^[Kindly refer to [Reference] for further reading.] compares the `model = c('DCC', 'aDCC')` but not `model = 'FDCC'` with all distributions and concludes that `aDCC` with `distribution = 'mvt'` is the best fit model and distribution for multivariate GARCH model. Here I directly use `mvt` but in different `solver` parameters.
The paper [Binary.com Interview Q1 - Comparison of Univariate GARCH Models](https://rpubs.com/englianhu/binary-Q1Uni-GARCH) describes the GARCH orders. [How to identify the ARCH and GARCH lag length in dynamic conditional correlation GARCH model?](https://stats.stackexchange.com/questions/136302/how-to-identify-the-arch-and-garch-lag-length-in-dynamic-conditional-correlation?answertab=votes#tab-top) describes the GARCH(1,1) and also DCC-GARCH as well.
<span style='color:goldenrod'>*Multivariate DCC-GARCH Model*</span> introduce the DCC and CCC models. In all tests for marginal goodness of fit the DCC-GARCH with skew Student's t-distributed errors outperformed the DCC-GARCH with Gaussian and Student's t-distributed errors. Comparing the DCC-GARCH model with the CCC-GARCH model using the Kupiec test showed that the DCC-GARCH model gave a better fit to the data.
#### VAR and Robust
Below models will set `VAR=TRUE` <s>and `robust=FALSE`</s> and `VAR=FALSE` to test if it is more accurate.
> If you have a multivariate conditional mean specification (i.e. VAR) then you cannot have a univariate conditional mean specification (arma model)...they are mutually exclusive. In short, do not enter anything for mean.model in ugarchspec (include.mean is automatically set to FALSE if VAR is selected).
*source : [rmgarch:dccforecast() and mregfor](http://r.789695.n4.nabble.com/rmgarch-dccforecast-and-mregfor-td4675161.html) or [how to test significance of VAR coefficients in DCC GARCH Fit](http://r.789695.n4.nabble.com/how-to-test-significance-of-VAR-coefficients-in-DCC-GARCH-Fit-td4472274.html)*
> Currently the DCCfit object (returned from running dccfit) does not return all the information on the VAR (coefficients can be extracted by looking at the model slot and 'varcoef' list i.e. fit at model$varcoef).
>
> A better approach is to first estimate the VAR model using the function 'varxfit' in the package which returns the standard errors and all relevant information, and then passing this returned object to the dccfit routine (example follows).
```
#################
library(rmgarch)
data(dji30ret)
Data = dji30ret[, 1:3, drop = FALSE]
vfit = varxfit(X=Data, p=1, exogen = NULL, robust = FALSE,
gamma = 0.25, delta = 0.01, nc = 10, ns = 500, postpad = "constant")
uspec = ugarchspec(mean.model = list(armaOrder = c(0,0), include.mean =
FALSE), variance.model = list(garchOrder = c(1,1), model = "sGARCH"),
distribution.model = "norm")
spec = dccspec(uspec = multispec( replicate(3, uspec) ), VAR = TRUE,
lag = 1, dccOrder = c(1,1), asymmetric = FALSE, distribution = "mvnorm")
fit = dccfit(spec, data = Data, fit.control = list(eval.se=TRUE),
VAR.fit = vfit)
#################
```
> The package also includes for convenience the 'varxfilter', 'varxforecast' and 'varxsim' functions which are used by the multivariate garch routines internally.
>
> As mentioned in the documentation, a comprehensive list of examples are included in the 'inst/rmgarch.tests' folder of the package.
>
> Regards,
>
> Alexios
*source : [[R-SIG-Finance] how to test significance of VAR coefficients in DCC GARCH Fit](https://stat.ethz.ch/pipermail/r-sig-finance/2012q1/009792.html)*
```{r dcc-var, eval=FALSE}
.VARs = c(TRUE, FALSE)
#.rb = c(TRUE, FALSE)
```
### Hi-Lo
#### `DCC` and `VAR=FALSE`
```{r DCC-HLVARF, message=FALSE, warning=FALSE, eval=FALSE}
## ------------- Simulate mv_fx() ----------------------
## mv_fx just made the model and some argument flexible.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp')#, 'gosolnp')
## Hi-Lo.
Hi.base <- llply(mbase['USDJPY'], Hi)
Lo.base <- llply(mbase['USDJPY'], Lo)
HiLo.base <- c(Hi.base, Lo.base) %>% do.call(cbind, .) %>% na.omit
## only use USDJPY trading day.
timeID <- HiLo.base %>%
index %>% ymd %>%
.[. >= timeID0] %>%
c(., xts::last(.) + days(1))
tmID <- list.files('data/fx/USDJPY',
pattern = '^DCC.GARCH.USDJPY.HL.[0-9]{4}-[0-9]{2}-[0-9]{2}.rds') %>%
str_extract_all('[0-9]{4}-[0-9]{2}-[0-9]{2}') %>%
unlist %>% ymd
baseDT <- ymd('2013-01-01')
timeID %<>% .[!. %in% tmID] %>% .[-1]
timeID %<>% .[. > baseDT]
DCC.GARCH.USDJPY <- list()
for (dt in timeID) {
for (i in seq(cr_code[7])) {
smp <- HiLo.base#[[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)
dtr %<>% .[. > baseDT]
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
DCC.GARCH.USDJPY[[i]] <- tryCatch({ldply(md[1], function(y) {
df = tryCatch(
mv_fx(smp, .model = y, .solver = 'solnp', .currency = cr_code[7],#[i],
.price_type = 'HL', .VAR = FALSE, .cluster = .cl),
error = function(e) cat(paste0(y, '.HL.', 'solnp', ' error.\n')))
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC),
VaR = df$forecastVaR)
names(df) %<>% str_replace_all('[0-9]{4}.[0-9]{2}.[0-9]{2}', 'T1')
df
})}, error = function(e) NULL)
if (is.null(DCC.GARCH.USDJPY[[i]])) {
subdir <- 'USDJPY'
} else {
subdir <- substr(names(DCC.GARCH.USDJPY[[i]])[3], 1, 6)
}
if (!dir.exists(paste0('data/fx/', subdir)))
dir.create(paste0('data/fx/', subdir))
saveRDS(DCC.GARCH.USDJPY[[i]], paste0(
'data/fx/', subdir, '/DCC.GARCH.USDJPY.HL.',
unique(DCC.GARCH.USDJPY[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', subdir, '/DCC.GARCH.USDJPY.HL.',
unique(DCC.GARCH.USDJPY[[i]]$Date), '.rds saved!\n'))
}
}; rm(i)
}
```
#### `aDCC` and `VAR=FALSE`
```{r aDCC-HLVARF, message=FALSE, warning=FALSE, eval=FALSE}
## ------------- Simulate mv_fx() ----------------------
## mv_fx just made the model and some argument flexible.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp')#, 'gosolnp')
## Hi-Lo.
Hi.base <- llply(mbase['USDJPY'], Hi)
Lo.base <- llply(mbase['USDJPY'], Lo)
HiLo.base <- c(Hi.base, Lo.base) %>% do.call(cbind, .) %>% na.omit
## only use USDJPY trading day.
timeID <- HiLo.base %>%
index %>% ymd %>%
.[. >= timeID0] %>%
c(., xts::last(.) + days(1))
tmID <- list.files('data/fx/USDJPY',
pattern = '^aDCC.GARCH.USDJPY.HL.[0-9]{4}-[0-9]{2}-[0-9]{2}.rds') %>%
str_extract_all('[0-9]{4}-[0-9]{2}-[0-9]{2}') %>%
unlist %>% ymd
baseDT <- ymd('2013-01-01')
timeID %<>% .[!. %in% tmID] %>% .[-1]
timeID %<>% .[. > baseDT]
aDCC.GARCH.USDJPY <- list()
for (dt in timeID) {
for (i in seq(cr_code[7])) {
smp <- HiLo.base#[[names(cr_code)[i]]]
timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
if (dt %in% timeID2) {
dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
dtr %<>% .[. > baseDT]
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
aDCC.GARCH.USDJPY[[i]] <- tryCatch({ldply(md[2], function(y) {
df = tryCatch(
mv_fx(smp, .model = y, .solver = 'solnp', .currency = cr_code[7],#[i],
.price_type = 'HL', .VAR = FALSE, .cluster = .cl),
error = function(e) cat(paste0(y, '.HL.', 'solnp', ' error.\n')))
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC),
VaR = df$forecastVaR)
names(df) %<>% str_replace_all('[0-9]{4}.[0-9]{2}.[0-9]{2}', 'T1')
df
})}, error = function(e) NULL)
if (is.null(aDCC.GARCH.USDJPY[[i]])) {
subdir <- 'USDJPY'
} else {
subdir <- substr(names(aDCC.GARCH.USDJPY[[i]])[3], 1, 6)
}
if (!dir.exists(paste0('data/fx/', subdir)))
dir.create(paste0('data/fx/', subdir))
saveRDS(aDCC.GARCH.USDJPY[[i]], paste0(
'data/fx/', subdir, '/aDCC.GARCH.USDJPY.HL.',
unique(aDCC.GARCH.USDJPY[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', subdir, '/aDCC.GARCH.USDJPY.HL.',
unique(aDCC.GARCH.USDJPY[[i]]$Date), '.rds saved!\n'))
}
}; rm(i)
}
```
#### `FDCC` and `VAR=FALSE`
```{r FDCC-HLVARF, message=FALSE, warning=FALSE, eval=FALSE}
## ------------- Simulate mv_fx() ----------------------
## mv_fx just made the model and some argument flexible.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp')#, 'gosolnp')
## Hi-Lo.
Hi.base <- llply(mbase['USDJPY'], Hi)
Lo.base <- llply(mbase['USDJPY'], Lo)
HiLo.base <- c(Hi.base, Lo.base) %>% do.call(cbind, .) %>% na.omit
## only use USDJPY trading day.
timeID <- HiLo.base %>%
index %>% ymd %>%
.[. >= timeID0] %>%
c(., xts::last(.) + days(1))
tmID <- list.files('data/fx/USDJPY',
pattern = '^FDCC.GARCH.USDJPY.HL.[0-9]{4}-[0-9]{2}-[0-9]{2}.rds') %>%
str_extract_all('[0-9]{4}-[0-9]{2}-[0-9]{2}') %>%
unlist %>% ymd
baseDT <- ymd('2013-01-01')
timeID %<>% .[!. %in% tmID] %>% .[-1]
timeID %<>% .[. > baseDT]
FDCC.GARCH.USDJPY <- list()
for (dt in timeID) {
for (i in seq(cr_code[7])) {
smp <- HiLo.base#[[names(cr_code)[i]]]
timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
if (dt %in% timeID2) {
dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
dtr %<>% .[. > baseDT]
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
FDCC.GARCH.USDJPY[[i]] <- tryCatch({ldply(md[3], function(y) {
df = tryCatch(
mv_fx(smp, .model = y, .solver = 'solnp', .currency = cr_code[7],#[i],
.price_type = 'HL', .VAR = FALSE, .cluster = .cl),
error = function(e) cat(paste0(y, '.HL.', 'solnp', ' error.\n')))
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC),
VaR = df$forecastVaR)
names(df) %<>% str_replace_all('[0-9]{4}.[0-9]{2}.[0-9]{2}', 'T1')
df
})}, error = function(e) NULL)
if (is.null(FDCC.GARCH.USDJPY[[i]])) {
subdir <- 'USDJPY'
} else {
subdir <- substr(names(FDCC.GARCH.USDJPY[[i]])[3], 1, 6)
}
if (!dir.exists(paste0('data/fx/', subdir)))
dir.create(paste0('data/fx/', subdir))
saveRDS(FDCC.GARCH.USDJPY[[i]], paste0(
'data/fx/', subdir, '/FDCC.GARCH.USDJPY.HL.',
unique(FDCC.GARCH.USDJPY[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', subdir, '/FDCC.GARCH.USDJPY.HL.',
unique(FDCC.GARCH.USDJPY[[i]]$Date), '.rds saved!\n'))
}
}; rm(i)
}
```
### Hi-Lo-Cl
#### `DCC` and `VAR=FALSE`
```{r DCC-HLCVARF, message=FALSE, warning=FALSE, eval=FALSE}
## ------------- Simulate mv_fx() ----------------------
## mv_fx just made the model and some argument flexible.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp')#, 'gosolnp')
## Hi-Lo-Cl.
Hi.base <- llply(mbase['USDJPY'], Hi)
Lo.base <- llply(mbase['USDJPY'], Lo)
Cl.base <- llply(mbase['USDJPY'], Cl)
HiLoCl.base <- c(Hi.base, Lo.base, Cl.base) %>%
do.call(cbind, .) %>% na.omit
rm(Hi.base, Lo.base, Cl.base)
## only use USDJPY trading day.
timeID <- HiLoCl.base %>% index %>% ymd %>%
.[. >= timeID0] %>% c(., xts::last(.) + days(1))
tmID <- list.files('data/fx/USDJPY',
pattern = '^DCC.GARCH.USDJPY.HLC.[0-9]{4}-[0-9]{2}-[0-9]{2}.rds') %>%
str_extract_all('[0-9]{4}-[0-9]{2}-[0-9]{2}') %>%
unlist %>% ymd
baseDT <- ymd('2013-01-01')
timeID %<>% .[!. %in% tmID] %>% .[-1]
timeID %<>% .[. > baseDT]
DCC.GARCH.USDJPY <- list()
for (dt in timeID) {
for (i in seq(cr_code[7])) {
smp <- HiLoCl.base#[[names(cr_code)[i]]]
timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
if (dt %in% timeID2) {
dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
dtr %<>% .[. > baseDT]
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
DCC.GARCH.USDJPY[[i]] <- tryCatch({llply(md[1], function(y) {
df = tryCatch(
mv_fx(smp, .model = y, .solver = 'solnp', .currency = cr_code[7],#[i],
.price_type = 'HLC', .VAR = FALSE, .cluster = .cl),
error = function(e) cat(paste0(y, '.HLC.', 'solnp', ' error.\n')))
res = suppressAll(data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC)))
VaR = df$forecastVaR
names(res) %<>% str_replace_all('[0-9]{4}.[0-9]{2}.[0-9]{2}', 'T1')
names(VaR) %<>% str_replace_all('[0-9]{4}.[0-9]{2}.[0-9]{2}', 'T1')
return(list(res = res, VaR = VaR))
})[[1]]}, error = function(e) NULL)
if (is.null(DCC.GARCH.USDJPY[[i]])) {
subdir <- 'USDJPY'
} else {
subdir <- substr(names(DCC.GARCH.USDJPY[[i]]$res)[3], 1, 6)
}
if (!dir.exists(paste0('data/fx/', subdir)))
dir.create(paste0('data/fx/', subdir))
saveRDS(DCC.GARCH.USDJPY[[i]], paste0(
'data/fx/', subdir, '/DCC.GARCH.USDJPY.HLC.',
unique(DCC.GARCH.USDJPY[[i]]$res$Date), '.rds'))
cat(paste0(
'data/fx/', subdir, '/DCC.GARCH.USDJPY.HLC.',
unique(DCC.GARCH.USDJPY[[i]]$res$Date), '.rds saved!\n'))
}
}; rm(i)
}
```
#### `aDCC` and `VAR=FALSE`
```{r aDCC-HLCVARF, message=FALSE, warning=FALSE, eval=FALSE}
## ------------- Simulate mv_fx() ----------------------
## mv_fx just made the model and some argument flexible.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp')#, 'gosolnp')
## Hi-Lo-Cl.
Hi.base <- llply(mbase['USDJPY'], Hi)
Lo.base <- llply(mbase['USDJPY'], Lo)
Cl.base <- llply(mbase['USDJPY'], Cl)
HiLoCl.base <- c(Hi.base, Lo.base, Cl.base) %>%
do.call(cbind, .) %>% na.omit
rm(Hi.base, Lo.base, Cl.base)
## only use USDJPY trading day.
timeID <- HiLoCl.base %>% index %>% ymd %>%
.[. >= timeID0] %>% c(., xts::last(.) + days(1))
tmID <- list.files('data/fx/USDJPY',
pattern = '^aDCC.GARCH.USDJPY.HLC.[0-9]{4}-[0-9]{2}-[0-9]{2}.rds') %>%
str_extract_all('[0-9]{4}-[0-9]{2}-[0-9]{2}') %>%
unlist %>% ymd
baseDT <- ymd('2013-01-01')
timeID %<>% .[!. %in% tmID] %>% .[-1]
timeID %<>% .[. > baseDT]
aDCC.GARCH.USDJPY <- list()
for (dt in timeID) {
for (i in seq(cr_code[7])) {
smp <- HiLoCl.base#[[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)
dtr %<>% .[. > baseDT]
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
aDCC.GARCH.USDJPY[[i]] <- tryCatch({llply(md[2], function(y) {
df = tryCatch(
mv_fx(smp, .model = y, .solver = 'solnp', .currency = cr_code[7],#[i],
.price_type = 'HLC', .VAR = FALSE, .cluster = .cl),
error = function(e) cat(paste0(y, '.HLC.', 'solnp', ' error.\n')))
res = suppressAll(data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC)))
VaR = df$forecastVaR
names(res) %<>% str_replace_all('[0-9]{4}.[0-9]{2}.[0-9]{2}', 'T1')
names(VaR) %<>% str_replace_all('[0-9]{4}.[0-9]{2}.[0-9]{2}', 'T1')
return(list(res = res, VaR = VaR))
})[[1]]}, error = function(e) NULL)
if (is.null(aDCC.GARCH.USDJPY[[i]])) {
subdir <- 'USDJPY'
} else {
subdir <- substr(names(aDCC.GARCH.USDJPY[[i]]$res)[3], 1, 6)
}
if (!dir.exists(paste0('data/fx/', subdir)))
dir.create(paste0('data/fx/', subdir))
saveRDS(aDCC.GARCH.USDJPY[[i]], paste0(
'data/fx/', subdir, '/aDCC.GARCH.USDJPY.HLC.',
unique(aDCC.GARCH.USDJPY[[i]]$res$Date), '.rds'))
cat(paste0(
'data/fx/', subdir, '/aDCC.GARCH.USDJPY.HLC.',
unique(aDCC.GARCH.USDJPY[[i]]$res$Date), '.rds saved!\n'))
}
}; rm(i)
}
```
#### `FDCC` and `VAR=FALSE`
```{r FDCC-HLCVARF, message=FALSE, warning=FALSE, eval=FALSE}
## ------------- Simulate mv_fx() ----------------------
## mv_fx just made the model and some argument flexible.
md <- c('DCC', 'aDCC', 'FDCC')
sv <- c('solnp')#, 'gosolnp')
## Hi-Lo-Cl.
Hi.base <- llply(mbase['USDJPY'], Hi)
Lo.base <- llply(mbase['USDJPY'], Lo)
Cl.base <- llply(mbase['USDJPY'], Cl)
HiLoCl.base <- c(Hi.base, Lo.base, Cl.base) %>%
do.call(cbind, .) %>% na.omit
rm(Hi.base, Lo.base, Cl.base)
## only use USDJPY trading day.
timeID <- HiLoCl.base %>% index %>% ymd %>%
.[. >= timeID0] %>% c(., xts::last(.) + days(1))
tmID <- list.files('data/fx/USDJPY',
pattern = '^FDCC.GARCH.USDJPY.HLC.[0-9]{4}-[0-9]{2}-[0-9]{2}.rds') %>%
str_extract_all('[0-9]{4}-[0-9]{2}-[0-9]{2}') %>%
unlist %>% ymd
baseDT <- ymd('2013-01-01')
timeID %<>% .[!. %in% tmID] %>% .[-1]
timeID %<>% .[. > baseDT]
FDCC.GARCH.USDJPY <- list()
for (dt in timeID) {
for (i in seq(cr_code[7])) {
smp <- HiLoCl.base#[[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)
dtr %<>% .[. > baseDT]
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
FDCC.GARCH.USDJPY[[i]] <- tryCatch({llply(md[3], function(y) {
df = tryCatch(
mv_fx(smp, .model = y, .solver = 'solnp', .currency = cr_code[7],#[i],
.price_type = 'HLC', .VAR = FALSE, .cluster = .cl),
error = function(e) cat(paste0(y, '.HLC.', 'solnp', ' error.\n')))