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We consider a multivariate Markov-switching GARCH model which allows for regime-specific volatility dynamics, leverage effects, and correlation structures. Conditions for stationarity and expressions for the moments of the process are derived. A Lagrange Multiplier test against misspecification of the within-regime correlation dynamics is proposed, and a simple recursion for multi-step-ahead conditional covariance matrices is deduced. We use this methodology to model the dynamics of the joint distribution of global stock market and real estate equity returns. The empirical analysis highlights the importance of the conditional distribution in Markov-switching time series models. Specifications with Student’s  t  innovations dominate their Gaussian counterparts both in- and out-of-sample. The dominating specification appears to be a two-regime Student’s  t  process with correlations which are higher in the turbulent (high-volatility) regime.

A multivariate regime-switching GARCH model with an application to global stock market and real estate equity returns