Garch is a useful tool and it is relatively easy to estimate an univariate standard Garch(p,q) model
with only lagged volatility estimates and innovations, as many statistics/econometric package such
as SAS, Matlab, EView already has this function.
However, it is another story for a Garch model with exogenous variables, such as the following
Garch-in-mean model,with error term in Normal distribution or t-distribution.There is a dummy
for day-of-the-week or holiday effect.
R(t)=a+b*h(t)+residualR(t)
h(t)=alpha+beta*h(t-1)+lamda*sqr(residual(t-1))+ kappa*Dummy+residualh(t)
Other exogenous variables which people may think help explain the volatility may also be
present in the Garch model. The question is:
Do you think it is worthy adding more exogenous variables?
How to estimate the Garch with exogenous variables? Any software for the function available?
Sometimes, multivariate Garch model (in some way, it like a VAR(vector autoregression model with
garch/hecteroskedastic volatility) is used to find the interaction between several markets (spot, option, futures...)
simultaneously? These Multivariate garch model with exogenous variables are even difficult to estimate.