I cannot reconcile the log-likelihood of a Copula-GARCH model.

Below is a simple example where the marginal volatilities are constant (for

which I use iGARCH with beta1 = 1) and have Normal distribution; and the

copula is constant and Gaussian. In short, the model is that of

returns having multivariate Normal distribution with constant parameters.

I compare the likelihood from cgarchfit (= 5890.564) with the likelihood

using the multinormal density, with both mean and covariance taken from

cgarchfit (= 5896.262). They should be the same.

Any help understanding why I cannot reconcile this will be much

appreciated!

-----------------------------------------------------------

library(rmgarch)

library(mvtnorm)

data(dji30retw)

z.t <- dji30retw[, 1:3]

uspec.each <- ugarchspec(mean.model = list(armaOrder = c(0,0)),

variance.model = list(model = "iGARCH", garchOrder

= c(1,1)),

distribution.model = "norm",

fixed.pars = list(beta1 = 1, alpha1 = 0, omega =

0))

mspec <- cgarchspec(uspec = multispec(replicate(ncol(z.t), uspec.each)),

distribution.model = list(copula = "mvnorm", method =

"Kendall", time.varying = FALSE, transformation = "parametric"))

cgarch <- cgarchfit(spec = mspec, data = z.t, solver.control=list(trace=1))

likelihood(cgarch) # 5890.564

mu <- coef(cgarch, type = 'garch')

cov <- rcov(cgarch)[,,1]

sum(dmvnorm(z.t, mean = mu, sigma = cov, log = TRUE)) # 5896.262

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