Based on the code found at "http://www.estima.com/procs/GARCHMV.PRG" I programmed a bivariate VECM DCC GARCH model with a multivariate t distribution. Although it works well and its parameters are in an adequate range, I still have a question regarding the standardization of the residuals in this procedure:
In the two step method, I would first calculate the univariate GARCH equations, standardize the residuals with its corresponding variances and calculate the Covariance Matrix "Q" based on the standardized residuals, right?
Why is this procedure (standardization) not necessary/wrong when I estimate the mean equations and covariance matrices together? In the mentioned code above as well as in mine, only the residuals of the mean equation enter "Q" and the loglikelihood rather than the standardized ones.
Any explanation would be of great help.
Kind regards!
Standardization of residuals in a multivariate DCC GARCH mod
Re: Standardization of residuals in a multivariate DCC GARCH
The two step method gives consistent, but not (statistically) efficient estimators as it ignores the information from the correlations among processes. However, particularly as the number of variables gets larger, it is computationally more efficient, as it never tries to optimize more than three parameters at a time (assuming GARCH(1,1) processes). One of the selling points of DCC was that it could be applied (using the two-step method) to rather large sets of variables for which BEKK or DVECH would be infeasible, while not being as constrained in its dynamics as a CC model (which also can be estimated by a two-step process, but also is statistically more efficient when estimated jointly).