Markov-switching GARCH models in finance: a unifying framework with an application to the German stock market

Reher Gerrit, Wilfling Bernd

Abstract
In this paper we develop a unifying Markov-switching GARCH model which enables us (1) to specify complex GARCH equations in two distinct Markov-regimes, and (2) to model GARCH equations of different functional forms across the two Markov-regimes. To give a simple example, our flexible Markov-switching approach is capable of estimating an exponential GARCH (EGARCH) specification in the first and a standard GARCH specification in the second Markov-regime. We derive a maximum likelihood estimation framework and apply our general Markov-switching GARCH model to daily excess returns of the German stock market index DAX. Our empirical study has two major findings. First, our estimation results unambiguously indicate that our general model outperforms all conventional Markov-switching GARCH models hitherto estimated in the financial literature. Second, we find significant Markov-switching in the German stock market with substantially differing volatility structures across the regimes.

Keywords
Markov-switching models; GARCH models; dynamics of stock index returns