Statistics and Algorithms / GARCH Models / GARCH Models (Multivariate) /

MV GARCH Residuals

The RESIDS option is specifically for univariate models (it returns only a single SERIES), so there are different options for multivariate models. The residuals for those can be organized either as a VECTOR of SERIES (if the separate time series are of greater interest) or as a SERIES of VECTORS (if the cross-variable correlation at a particular time is of greatest interest). The first is done with the RSERIES option, which serves the same purpose as the RESIDS options on instructions like ESTIMATE and SUR. The second is done with the RVECTORS option, which creates a SERIES[VECTOR].

The following saves the residuals (using RSERIES) and the covariances (using MVHSERIES) and creates a dummy variable which is 1 if the residual for Japan is in the left .05 tail of the conditional distribution. (The FIXT is to correct for the difference between the standard t distribution and the rescaled t with unit variance used by GARCH).

garch(p=1,q=1,mv=bekk,pmethod=simplex,piters=10,distrib=t,$

rseries=rs,mvhseries=hhs) / xjpn xfra xsui

compute fixt=(%shape-2)/%shape

set trigger = %tcdf(rs(1)/sqrt(hhs(1,1)*fixt),%shape)<.05

sstats(mean) / trigger>>VaRp

disp "Probability of being below .05 level" #.#### VaRp