Covariance forecasts and long-run correlations in a Markov-switching model for dynamic correlations

Recently, Pelletier [2006. Journal of Econometrics 131, 445-473] proposed a model for dynamic correlations based on the idea to combine standard GARCH models for the volatilities with a Markov-switching process for the conditional correlations. In this paper, several properties of the model are derived. First, we provide a simple recursion for multi-step covariance forecasts under both Gaussian and Student's t innovations, which is much simpler to implement than the formula presented by Pelletier (2006) for normally distributed errors. Second, we derive expressions for the unconditional covariances and correlations and the cross correlation function of the absolute returns. An application to returns of international stock and real estate markets shows that correlations between these asset classes increased substantially during the recent financial turmoil; moreover, in the regime-switching framework, employing a Student's t distribution improves the forecasting performance vis-a`-vis the Gaussian.