A New Approach to Markov-Switching GARCH Models
University of Munich
University of Munich, Center for Financial Studies, and Ifo Institute for Economic Research
University of Zurich
Address correspondence to Stefan Mittnik, Chair of Financial Econometrics, Institute of Statistics, University of Munich, D-80799 Munich, Germany, or e-mail: finmetrics{at}stat.uni-muenchen.de.
The use of Markov-switching models to capture the volatility dynamics of financial time series has grown considerably during past years, in part because they give rise to a plausible interpretation of nonlinearities. Nevertheless, GARCH-type models remain ubiquitous in order to allow for nonlinearities associated with time-varying volatility. Existing methods of combining the two approaches are unsatisfactory, as they either suffer from severe estimation difficulties or else their dynamic properties are not well understood. In this article we present a new Markov-switching GARCH model that overcomes both of these problems. Dynamic properties are derived and their implications for the volatility process discussed. We argue that the disaggregation of the variance process offered by the new model is more plausible than in the existing variants. The approach is illustrated with several exchange rate return series. The results suggest that a promising volatility model is an independent switching GARCH process with a possibly skewed conditional mixture density.
KEYWORDS: conditional volatility, density forecasting, empirical finance, exchange rates, nonlinear time series, regime switching
Received March 18, 2004; revised July 2, 2004; accepted July 5, 2004
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