R - Modelling Multivariate GARCH (rugarch and ccgarch)

Question

First time asking a question here, I'll do my best to be explicit - but let me know if I should provide more info! Second, that's a long question...hopefully simple to solve for someone ;)! So using "R", I'm modelling multivariate GARCH models based on some paper (Manera et al. 2012).

I model the Constant Conditional Correlation (CCC) and Dynamic Conditional Correlation (DCC) models with external regressors in the mean equations; using "R" version 3.0.1 with package "rugarch" version 1.2-2 for the univariate GARCH with external regressors, and "ccgarch" package (version 0.2.0-2) for the CCC/DCC models. (I'm currently looking into the "rmgarch" package - but it seems to be only for the DCC and I need CCC model too.)

I have problem in the mean equations of my models. In the paper that I mentionned above, the parameter estimates of the mean equation between the CCC and DCC models changes! And I don't know how I would do that in R... (currently, looking on Google and into Tsay's book "analysis of financial time series" and Engle's book "Anticipating correlations" to find my mistake)

What I mean by "my mean equations don't change between CCC and DCC models", it the following: I specify the univariate GARCH for my n=5 time series with the package rugarch. Then, I use the estimates parameters of the GARCH (ARCH + GARCH terms) and use them for both the CCC and DCC functions "eccc.sim()" and "dcc.sim()". Then, from eccc.estimation() and dcc.estimation() functions, I can retrieve the estimates for the variance equations as well as the correlation matrices. But not for the mean equation.

I post the R-code (reproducible and my original one) for univariate models and the CCC model only. Thank you already for reading my post!!!!!

Note: in the code below, "data.repl" is a "zoo" object of dim 843x22 (9 daily Commodities returns series and explanatory variables series). The multivariate GARCH is for 5 series only.

Reproducible code:

# libraries:
library(rugarch)
library(ccgarch)
library(quantmod)
# Creating fake data:
dataRegr <- matrix(rep(rnorm(3149,  11, 1),1), ncol=1, nrow=3149)
dataFuelsLag1 <- matrix(rep(rnorm(3149, 24, 8),2), ncol=2, nrow=3149)
#S&P 500 via quantmod and Yahoo Finance
T0 <- "2000-06-23"
T1 <- "2012-12-31"
getSymbols("^GSPC", src="yahoo", from=T0, to=T1)
sp500.close <- GSPC[,"GSPC.Close"], 
getSymbols("UBS", src="yahoo", from=T0, to=T1)
ubs.close <- UBS[,"UBS.Close"]
dataReplic <- merge(sp500.close, ubs.close, all=TRUE)
dataReplic[which(is.na(dataReplic[,2])),2] <- 0  #replace NA

### (G)ARCH modelling ###
#########################
# External regressors: macrovariables and all fuels+biofuel Working's T index
ext.regr.ext <- dataRegr
regre.fuels <- cbind(dataFuelsLag1, dataRegr)
### spec of GARCH(1,1) spec with AR(1) ###
garch11.fuels <- as.list(1:2)
for(i in 1:2){
  garch11.fuels[[i]] <- ugarchspec(mean.model = list(armaOrder=c(1,0), 
                                                     external.regressors = as.matrix(regre.fuels[,-i])))
}

### fit of GARCH(1,1) AR(1) ###
garch11.fuels.fit <- as.list(1:2)
for(i in 1:2){
  garch11.fuels.fit[[i]] <- ugarchfit(garch11.fuels[[i]], dataReplic[,i])
}
##################################################################
#### CCC fuels: with external regression in the mean eqaution ####
##################################################################
nObs <- length(data.repl[-1,1])
coef.unlist <- sapply(garch11.fuels.fit, coef)
cccFuels.a <- rep(0.1, 2)
cccFuels.A <- diag(coef.unlist[6,])
cccFuels.B <- diag(coef.unlist[7, ])
cccFuels.R <- corr.test(data.repl[,fuels.ind], data.repl[,fuels.ind])$r

# model=extended (Jeantheau (1998))
ccc.fuels.sim <- eccc.sim(nobs = nObs, a=cccFuels.a, A=cccFuels.A,
                          B=cccFuels.B, R=cccFuels.R, model="extended")
ccc.fuels.eps <- ccc.fuels.sim$eps
ccc.fuels.est <- eccc.estimation(a=cccFuels.a, A=cccFuels.A,
                                 B=cccFuels.B, R=cccFuels.R,
                                 dvar=ccc.fuels.eps, model="extended")
ccc.fuels.condCorr <- round(corr.test(ccc.fuels.est$std.resid,
                                      ccc.fuels.est$std.resid)$r,digits=3)

My original code:

### (G)ARCH modelling ###
#########################
# External regressors: macrovariables and all fuels+biofuel Working's T index
ext.regr.ext <- as.matrix(data.repl[-1,c(10:13, 16, 19:22)])
regre.fuels <- cbind(fuel.lag1, ext.regr.ext) #fuel.lag1 is the pre-lagged series
### spec of GARCH(1,1) spec with AR(1) ###
garch11.fuels <- as.list(1:5)
for(i in 1:5){
  garch11.fuels[[i]] <- ugarchspec(mean.model = list(armaOrder=c(1,0),
                                   external.regressors = as.matrix(regre.fuels[,-i])))
}# regre.fuels[,-i] => "-i" because I model an AR(1) for each mean equation

### fit of GARCH(1,1) AR(1) ###
garch11.fuels.fit <- as.list(1:5)
for(i in 1:5){
  j <- i
  if(j==5){j <- 7} #because 5th "fuels" is actually column #7 in data.repl
  garch11.fuels.fit[[i]] <- ugarchfit(garch11.fuels[[i]], as.matrix(data.repl[-1,j])))
}

#fuelsLag1.names <- paste(cmdty.names[fuels.ind], "(-1)")
fuelsLag1.names <- cmdty.names[fuels.ind]
rowNames.ext <- c("Constant", fuelsLag1.names, "Working's T Gasoline", "Working's T Heating Oil",
              "Working's T Natural Gas", "Working's T Crude Oil",
              "Working's T Soybean Oil", "Junk Bond", "T-bill", 
              "SP500", "Exch.Rate")
ic.n <- c("Akaike", "Bayes")
garch11.ext.univSpec <- univ.spec(garch11.fuels.fit, ols.fit.ext, rowNames.ext, 
                                  rowNum=c(1:15), colNames=cmdty.names[fuels.ind],
                                  ccc=TRUE)
##################################################################
#### CCC fuels: with external regression in the mean eqaution ####
##################################################################
# From my GARCH(1,1)-AR(1) model, I extract ARCH and GARCH
# in order to model a CCC GARCH model:
nObs <- length(data.repl[-1,1])
coef.unlist <- sapply(garch11.fuels.fit, coef)

cccFuels.a <- rep(0.1, length(fuels.ind))
cccFuels.A <- diag(coef.unlist[17,])
cccFuels.B <- diag(coef.unlist[18, ])
#based on Engle(2009) book, page 31:
cccFuels.R <- corr.test(data.repl[,fuels.ind], data.repl[,fuels.ind])$r

# model=extended (Jeantheau (1998))
# "allow the squared errors and variances of the series to affect
# the dynamics of the individual conditional variances
ccc.fuels.sim <- eccc.sim(nobs = nObs, a=cccFuels.a, A=cccFuels.A,
                                   B=cccFuels.B, R=cccFuels.R, model="extended")
ccc.fuels.eps <- ccc.fuels.sim$eps
ccc.fuels.est <- eccc.estimation(a=cccFuels.a, A=cccFuels.A,
                                          B=cccFuels.B, R=cccFuels.R,
                                          dvar=ccc.fuels.eps, model="extended")
ccc.fuels.condCorr <- round(corr.test(ccc.fuels.est$std.resid,
                                      ccc.fuels.est$std.resid)$r,digits=3)
colnames(ccc.fuels.condCorr) <- cmdty.names[fuels.ind]
rownames(ccc.fuels.condCorr) <- cmdty.names[fuels.ind]
lowerTri(ccc.fuels.condCorr, rep=NA)

Answer 1

Are you aware that there is a whole package rmgarch for multivariate GARCH models?

Per its DESCRIPTION, it covers

Feasible multivariate GARCH models including DCC, GO-GARCH and Copula-GARCH.