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?

  • $\begingroup$ If the confidence bounds are adjusted appropriately for the fact that these are residuals, not raw data, then it looks like MS-GARCH fits the data less well than GARCH. Wouldn't that be what you would have deduced had you not asked this question? $\endgroup$ – Richard Hardy Apr 24 '18 at 15:57
  • $\begingroup$ @RichardHardy please see the edited question because I did not explain myself well. $\endgroup$ – Anna Apr 24 '18 at 16:03
  • $\begingroup$ Can it be that AIC and BIC are not comparable across the models because some constants are omitted in likelihood calculations? Software packages sometimes omit constants from likelihood calculation but sometimes they do not, so you have to be careful when comparing results across packages. You could try calculating the likelihood manually from the standardized residuals (taking the sum of the logarithms of their probability densities) to see if they match across the packages. $\endgroup$ – Richard Hardy Apr 24 '18 at 17:31
  • $\begingroup$ @RichardHardy I am using the same package for the fitting of the models so I do not think that is the issue $\endgroup$ – Anna Apr 24 '18 at 17:39

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