hello, i'm a phd student, i would like to ask for your help in undertanding the diffrence between studying Spillover in the mean and volatility using BEKK ( for exemple ) and VAR-BEKK ? what is the advantage that VAR-BEKK model have over BEKK model to study this phenomenon ?
and thanks in advance
BEKK or any MGARCH focuses on the variance and covariance matrix, and the VAR part is where you model the return series
The BEKK model refers to the part when you are modelling the conditional variance. However, you cannot model conditional variance without modelling returns. Therefore, any BEKK model is always XXX-BEKK model. The XXX part can have various specifications. In many cases, you can assume that mean returns to e.g. a) be zero, b) be some constants, c) follow AR(1) processes, d) follow VAR process, e) ...or something else.
For daily returns of a liquid asset, it is often sufficient to assume zero or constant mean, because average daily returns are much smaller than their standard deviation (therefore you can assume zero) or some constant (because daily returns are close to unpredictable). However, if you are using the model for some macro data, then the dynamics might be much more complicated, and you might need VAR model for modelling conditional means.
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