# R/simulateDCC.R In ccgarch2: Conditional Correlation GARCH Models

#### Documented in simulateDCC

```###################################################################
# simulating data from DCC-GARCH(1, 1) DGP
simulateDCC <- function(a, b, Q, a0, A, B, nobs, ncut=1000){
nobs <- nobs + ncut             # ncut is the number of observations to be removed
ndim <- nrow(Q)

const <- (1-a-b)*Q

z <- diag(0, nobs, ndim)
DCC <- diag(0, nobs, ndim^2)
vecQ2 <- diag(0, nobs, ndim^2)
Q2 <- Q         # initial value of Q0
zz <- Q
h <- diag(0, nobs, ndim)
eps <- diag(0, nobs, ndim)
ht <- rep(0, ndim)
et2 <- rep(0, ndim)
for(i in 1:nobs){
Q2 <- const + a*zz + b*Q2
invdQ2 <- diag(1/sqrt(diag(Q2)))
D2 <- invdQ2%*%Q2%*%invdQ2
DCC[i, ] <- as.vector(D2)
vecQ2[i, ] <- as.vector(Q2)

# zt <- mvrnorm(1, rep(0, ndim), D2)     # standardized residual sdampling from N(0, R_t) whereR_t = D2 is DCC at t
#############################################
cholD2 <- t(chol(D2))
zt <- drop(cholD2%*%rnorm(ndim))
#############################################
zz <- zt%o%zt
z[i, ] <- zt

ht <- a0 + A%*%et2 + B%*%ht           # conditional variance at t
h[i, ] <- drop(ht)
eps[i, ] <- zt*sqrt(ht)               # simulated observation at t
et2 <- eps[i, ]^2
}

# A character vector/matrix for naming parameters
name.id <- as.character(1:ndim)
namev <- diag(0, ndim, ndim)
for(i in 1:ndim){
for(j in 1:ndim){
namev[i, j] <- paste(name.id[i], name.id[j], sep="")
}
}
# naming rows
rownames(DCC) <- c(rep(0, ncut), 1:(nobs-ncut))
rownames(vecQ2) <- c(rep(0, ncut), 1:(nobs-ncut))
rownames(z) <- c(rep(0, ncut), 1:(nobs-ncut))
rownames(h) <- c(rep(0, ncut), 1:(nobs-ncut))
rownames(eps) <- c(rep(0, ncut), 1:(nobs-ncut))
# naming columns
colnames(DCC) <- paste("R", namev, sep="")
colnames(vecQ2) <- paste("R", namev, sep="")
colnames(z) <- paste("Series", name.id, sep="")
colnames(h) <- paste("Series", name.id, sep="")
colnames(eps) <- paste("Series", name.id, sep="")

list(DCC=zoo(DCC[-(1:ncut), ]), z=zoo(z[-(1:ncut), ]), Q=zoo(vecQ2[-(1:ncut), ]), h=zoo(h[-(1:ncut), ]), eps=zoo(eps[-(1:ncut), ]))
}

###################################################################
# simulating data from DCC-GARCH(1, 1) DGP with GJR-type asymmetry
simulateDCC.lev <- function(a, b, Q, a0, A, B, Lev, nobs, ncut=1000){
nobs <- nobs + ncut             # ncut is the number of observations to be removed
ndim <- nrow(Q)

const <- (1-a-b)*Q

z <- diag(0, nobs, ndim)
DCC <- diag(0, nobs, ndim^2)
vecQ2 <- diag(0, nobs, ndim^2)
Q2 <- Q         # initial value of Q0
zz <- Q
h <- diag(0, nobs, ndim)
eps <- diag(0, nobs, ndim)
ht <- rep(0, ndim)
et2 <- rep(0, ndim)
for(i in 1:nobs){
Q2 <- const + a*zz + b*Q2
invdQ2 <- diag(1/sqrt(diag(Q2)))
D2 <- invdQ2%*%Q2%*%invdQ2
DCC[i, ] <- as.vector(D2)
vecQ2[i, ] <- as.vector(Q2)

zt <- mvrnorm(1, rep(0, ndim), D2)     # sdampling from N(0m R_t) where R_t is DCC at t
zz <- zt%o%zt
z[i, ] <- zt

ind <- (-sign(zt)+1)/2

ht <- a0 + A%*%et2 + B%*%ht + Lev%*%(ind*et2)           # conditional variange at t
h[i, ] <- drop(ht)
eps[i, ] <- zt*sqrt(ht)               # simulated observation at t
et2 <- eps[i, ]^2
}
# A character vector/matrix for naming parameters
name.id <- as.character(1:ndim)
namev <- diag(0, ndim, ndim)
for(i in 1:ndim){
for(j in 1:ndim){
namev[i, j] <- paste(name.id[i], name.id[j], sep="")
}
}
# naming rows
rownames(DCC) <- c(rep(0, ncut), 1:(nobs-ncut))
rownames(vecQ2) <- c(rep(0, ncut), 1:(nobs-ncut))
rownames(z) <- c(rep(0, ncut), 1:(nobs-ncut))
rownames(h) <- c(rep(0, ncut), 1:(nobs-ncut))
rownames(eps) <- c(rep(0, ncut), 1:(nobs-ncut))
# naming columns
colnames(DCC) <- paste("R", namev, sep="")
colnames(vecQ2) <- paste("R", namev, sep="")
colnames(z) <- paste("Series", name.id, sep="")
colnames(h) <- paste("Series", name.id, sep="")
colnames(eps) <- paste("Series", name.id, sep="")

#  list(DCC=DCC[-(1:ncut), ], z=z[-(1:ncut), ], Q=vecQ2[-(1:ncut), ], h=h[-(1:ncut), ], eps=eps[-(1:ncut), ])
list(DCC=zoo(DCC[-(1:ncut), ]), z=zoo(z[-(1:ncut), ]), Q=zoo(vecQ2[-(1:ncut), ]), h=zoo(h[-(1:ncut), ]), eps=zoo(eps[-(1:ncut), ]))
}
```

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ccgarch2 documentation built on May 31, 2017, 4:23 a.m.