I am checking different GARCH models for my financial time series. What I have noticed is that regression coefficients in mean equation change considerably when different GARCH models are applied. Is it normal?
I am not an expert, but my intuition tells me that changes shouldn't be dramatic. Maybe my model is bad?
By the way, when I tried checking the best model using AIC/BIC; they all were approximately same, but coefficients considerably different.
Since AR models can approximate MA models and vice versa, two models with quite different coefficients might describe very similar processes. You could check this by examining impulse-response functions which is a more transparent approach than looking at the coefficients directly, unless the model has very few lags. An indication of the phenomenon could be that the likelihoods of the different models are close. If the number of parameters is about the same in the different models, then also the AIC and BIC values would be close across models, something that you have reported.
Adding a GARCH conditional variance equation to the model might result in a jump from one approximation of the conditional mean to another one that look different but are actually similar. On the other hand, depending on the strength of the GARCH pattern there might occasionally be substantial large changes in the estimated conditional mean process, though I agree that normally you would not expect them to be dramatic.
