Testing the Dependence Structure of the Components of Hybrid Processes Using Mutual Information

Mutual information is a useful extension of the correlation coecient to study the dependence among multiple random processes. Hybrid processes are multivariate time series with some components continuous time series and the rest point processes. Assessment of the strength of the dependence structure amongst the components of hybrid processes are usually done by various linear methods which often prove inadequate. In this paper mutual information is studied for bivariate stationary hybrid processes. Results on convergence of the mutual information estimates for bivariate time series are developed. It is shown that the mutual information statistic can be super-optimal compared to the class of non-parametric estimates discussed in Stone (1980).