I am fitting a GARCH model as well as a Markov-switching GARCH model on a time series. When checking the ACF plots of the squared standardised residuals quite a number of lags fall outside the confidence bands in case of MS GARCH while in case of GARCH, only 2 fall outside the confidence bands.
However when looking at the AIC and BIC the MS GARCH model gives lower values (thus it is superior). Also looking at the data we can see that regimes (different periods of volatility) exist. Why do the AIC and BIC prefer MS GARCH model when it is not capable as good as the GARCH in eliminating the autocorrelation?