(there were some mistakes in the previous code, I've corrected it and I'm
reposting)
I'm trying to simulate 1-step ahead returns 5000 times for a portfolio of 9
variables. After specifying their GJR-GARCH specifications with SPD marginals,
I use the following code (which was inspired by the examples in the
'rmgarch.tests' folder). I use the first 571x9 observations for fitting and the
last 570 for out-of-sample analysis. Moreover, I use a moving-window approach,
in the sense that I always use the last 571 observations in the cgarchfilter
rather than [1:(T+i)] as in the example. Once the simulated returns 'simx' are
stored in 'simulatedreturns', I compute the return of an equally-weighted
portfolio as a 570x5000 matrix, i.e. one series of return of each observation
for each simulation. Last, I compute VaR (90%, 95%, 99%) as the respective
quantile (0.10, 0.05, 0.01).
My problem is that, contrary to the literature I've found on the topic, VaR is
severely underestimated, I obtain a number of violations which is way more than
expected (should be 57 for 90%VaR, 28 for 95%VaR, 6 for 99%VaR). Is there any
error in the code I have below? I've followed the example by the letter and
cannot understand what went wrong. Anyone can help? Any hint is GREATLY
appreciated!
library(rugarch)
library(rmgarch)
data(dji30retw)
Dat = dji30retw[, 1:9, drop = FALSE]
model <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(1,1),
variance.targeting=TRUE),
mean.model=list(armaOrder=c(0,0), include.mean=F, archm=F,
archpow=1),
distribution.model="norm")
spec = cgarchspec(uspec = multispec(replicate(9, model)), VAR = FALSE, robust =
FALSE,
lag.criterion = "AIC", external.regressors = NULL,
dccOrder = c(1,1), asymmetric = TRUE, distribution.model =
list(copula = "mvt",
method = "ML", time.varying = TRUE,
transformation = "spd"))
fit = cgarchfit(spec, data = Dat, out.sample = 570, cluster = NULL, spd.control
= list(lower = 0.1, upper = 0.9, type = "mle", kernel = "normal"),
fit.control = list(eval.se=FALSE))
T = dim(Dat)[1]-570
simMu = simS = filtMu = filtS = matrix(NA, ncol = 9, nrow = 570)
simCor = simC = filtC = filtCor = array(NA, dim = c(9,9,570))
colSd = function(x) apply(x, 2, "sd")
specx = spec
for(i in 1:9) specx@umodel$fixed.pars[[i]] =
as.list(fit@model$mpars[fit@model$midx[,i]==1,i])
setfixed(specx)<-as.list(fit@model$mpars[fit@model$midx[,10]==1,10])
simulatedreturns <- array(dim=c(570,9,5000))
for(i in 1:570){
if(i==1){
presigma = matrix(tail(sigma(fit), 1), ncol = 9)
prereturns = matrix(unlist(Dat[T, ]), ncol = 9, nrow = 1)
preresiduals = matrix(tail(residuals(fit),1), ncol = 9, nrow = 1)
preR = last(rcor(fit))[,,1]
diag(preR) = 1
preQ = fit@mfit$Qt[[length(fit@mfit$Qt)]]
preZ = tail(fit@mfit$Z, 1)
tmp = cgarchfilter(specx, Dat[2:(T+1), ], filter.control = list(n.old = T))
filtMu[i,] = tail(fitted(tmp), 1)
filtS[i,] = tail(sigma(tmp), 1)
filtC[,,i] = last(rcov(tmp))[,,1]
filtCor[,,i] = last(rcor(tmp))[,,1]
} else{
presigma = matrix(tail(sigma(tmp), 1), ncol = 9)
prereturns = matrix(unlist(Dat[(T+i-1), ]), ncol = 9, nrow = 1)
preresiduals = matrix(tail(residuals(tmp),1), ncol = 9, nrow = 1)
preR = last(rcor(tmp))[,,1]
diag(preR) = 1
preQ = tmp@mfilter$Qt[[length(tmp@mfilter$Qt)]]
preZ = tail(tmp@mfilter$Z, 1)
tmp = cgarchfilter(specx, Dat[(i+1):(T+i), ], filter.control = list(n.old =
T))
filtMu[i,] = tail(fitted(tmp), 1)
filtS[i,] = tail(sigma(tmp), 1)
filtC[,,i] = last(rcov(tmp))[,,1]
filtCor[,,i] = last(rcor(tmp))[,,1]
}
sim = cgarchsim(fit, n.sim = 1, m.sim = 5000, startMethod = "sample", preR =
preR, preQ = preQ, preZ = preZ,
prereturns = prereturns, presigma = presigma, preresiduals
= preresiduals, cluster = NULL)
simx = t(sapply(sim@msim$simX, FUN = function(x) x[1,]))
simMu[i,] = colMeans(simx)
simC[,,i] = sim@msim$simH[[1]][,,1]
simCor[,,i] = sim@msim$simR[[1]][,,1]
simS[i,] = sqrt(diag(simC[,,i]))
simulatedreturns[i,,]=simx
}
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