Testing causality between two vectors in multivariate GARCHÂ models

The family of Constant Conditional Correlation GARCH models is used to model the risk associated with financial time series and to make inferences about Granger-causal relationships between second conditional moments. The restrictions for second-order Granger noncausality between two vectors of variables are derived and assessed using posterior odds ratios. This Bayesian method constitutes an alternative to classical tests and can be employed regardless of the form of the restrictions on the parameters of the model. This approach enables the assumptions about the existence of higher-order moments of the processes that are required in classical tests to be relaxed. In the empirical example, a bidirectional second-order causality between the pound-to-Euro and US dollar-to-Euro exchange rates is found.