Regime switching for dynamic correlations

We propose a new model for the variance between multiple time series, the regime switching dynamic correlation. We decompose the covariances into correlations and standard deviations and the correlation matrix follows a regime switching model; it is constant within a regime but different across regimes. The transitions between the regimes are governed by a Markov chain. This model does not suffer from a curse of dimensionality and it allows analytic computation of multi-step ahead conditional expectations of the variance matrix when combined with the ARMACH model (Taylor (Modelling Financial Time Series. Wiley, New York) and Schwert (J. Finance 44(5) (1989) 1115)) for the standard deviations. We also present an empirical application which illustrates that our model can have a better fit of the data than the dynamic conditional correlation model proposed by Engle (J. Business Econ. Statist. 20(3) (2002) 339).