Testing for the number of regimes in financial time series GARCH Volatility

In this paper, we investigate the test of the optimal number of regimes which can describe better the corresponding conditional variance to different stock market indices. We compared several GARCH models using
the Deviance Information Criterion (DIC), provided by the Bayesian approach Markov chain Monte Carlo
(MCMC), taking into consideration many stylized facts such as leverage effect, fat-tailed distributions and volatility clustering. The results show clearly that the four selected models exhibit a leverage effect and have at least two regimes whatever the GARCH specifications are. And the optimal number of regimes in
conditional variance process may change from a series to another depending on their structure. A predictive test using the Value-at-Risk confirms that the selected processes provide accurate volatility forecasts.
Keywords: MS GARCH, Bayesian Approach, DIC, Conditional Variance, Switching-Regimes, Stock
Market Indices