344 LARGE AND SMALL CAP STOCKS IN EUROPEthe CAC40 come together. In addition, the covariance surface is quite flat,
increasing as negative shocks in the MIDCAC take larger values. Finally, it
can be observed that the beta coefficient surface is quite stable.
Panel (B) of Figure 17.3 displays the news impact surfaces for the German
market. It can be appreciated that the DAX variance surface shows a clear
asymmetry; variance increases the most when both shocks are of the same
sign. In addition, this increase is larger when both shocks are negative. The
SDAX variance increases the most when both the large stock index shock
and the small stock index shock are of the same sign. Moreover, covariance
only increases when both shocks are of the same sign. When shocks are cross-
signed, covariance slightly decreases. Finally, it can be appreciated that the
beta coefficient has the expected behavior, it increases with the shock size
when both socks are of the same sign and decreases when shocks are of
different sign.
Panel (C) of Figure 17.3 displays the news impact surfaces for the British
market. It can be seen that the FTSE variance increases the most when cross-
signed shocks take place or, when both shocks are negative. The SMALL
CAP variance increases the most when both shocks are negative. Moreover
the covariance surface shows a clear asymmetry; the covariance increases
when both shocks are of the same sign whereas decreases when shocks are of
different sign. Finally, the beta coefficient surface is very sensitive to extreme
positive shocks in the small cap index.
17.5.2 Robust conditional moment test
The robust conditional moment test of Wooldridge (1990) is applied to
test how the Glostenet al. (1993) modification to the multivariate GARCH
model cleans the asymmetries in the conditional covariance matrix. This
test enables the identification of possible sources of misspecification in
the model and is robust to distributional assumptions. In order to test
the validity of a model, a natural approach is to compare theex post
cross-product matrix of the residuals (
√
T-consistent estimator) to the
estimated covariance matrix. Thus, Kroner and Ng (1998) define a “gen-
eralized residual” asvijt=εitεjt−hijtfor alli,j=1, 2. If the model is correct,
Et− 1 (vijt)=0, and thereforevijtshould be uncorrelated with any variable
known at timet−1. These variables are called misspecification indicators.
Kroner and Ng (1998) use three kinds of misspecification indicators. These
indicators try to detect misspecification caused by shocks’ sign (I(ε 1 t<0)
andI(ε 2 t<0)), the four quadrant sign combinations (I(ε 1 t− 1 >0;ε 2 t− 1 >0),
I(ε 1 t− 1 <0;ε 2 t− 1 >0), I(ε 1 t− 1 >0;ε 2 t− 1 <0), I(ε 1 t− 1 <0;ε 2 t− 1 <0)) and
the misspecification due to the cross effects of shocks’ size and sign
(ε^21 t− 1 I(ε 1 t− 1 <0),ε^21 t− 1 I(ε 2 t− 1 <0),ε^22 t− 1 I(ε 1 t− 1 <0),ε^22 t− 1 (ε 2 t− 1 <0)).I(.)
denotes an indicator function that equals one if the argument is true and zero