Bayesian Testing of Granger Causality in Markov-Switching VARs

Recent economic developments have shown the importance of spillover and contagion effects in financial markets as well as in macroeconomic reality. Such effects are not limited to relations between the levels of variables but also impact on the volatility and the distributions. We propose a method of testing restrictions for Granger noncausality on all these levels in the framework of Markov-switching Vector Autoregressive Models. The conditions for Granger noncausality for these models were derived by Warne (2000). Due to the nonlinearity of the restrictions, classical tests have limited use. We, therefore, choose a Bayesian approach to testing. The inference consists of a novel Gibbs sampling algorithm for estimation of the restricted models, and of standard methods of computing the Posterior Odds Ratio. The analysis may be applied to financial and macroeconomic time series with complicated properties, such as changes of parameter values over time and heteroskedasticity.