Testing for the Number of Regimes in Financial Time Series GARCH Volatility

Abstract

This paper investigates the optimal number of regimes that can better describe the corresponding conditional variance to different stock market indices. We compared several GARCH specifications using the Deviance Information Criterion (DIC), provided by the Bayesian approach Markov chain Monte Carlo (MCMC), considering many stylized facts such as asymmetry (i.e., 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. In addition, the optimal number of regimes in the 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.