I am trying to estimate ARMA-GARCH model for my stock returns time series.
I have estimated ARMA model for my series, and found that there exists ARCH, so added GARCH(1,1) term. However I now find previously significant ARMA coefficients being insignificant.
In this case, should I remove the insignificant ARMA terms? I am reluctant in doing so as I read from a book that it is not wise to remove ARMA terms judging from their significance.
Also, as I am not performing any predictions with this model (only using it as a normal return model for event study), I thought it would be unnecessary to do so?