Assessing the Dependence Structure of the Components of Hybrid Time Series Processes Using Mutual Information

Abstract

Hybrid processes, which are multivariate time series with some components continuous valued time series and the rest discrete valued time series or point processes, often arise in studies of neurological systems. Assessment of the dependence structure among the components of hybrid processes are usually done by various linear methods which often prove inadequate. Mutual information (MI) is a useful extension of the correlation coefficient to study such structures. In this paper we consider the application of MI to study the dependence structure of bivariate stationary hybrid processes. We develop results on the asymptotic behaviour of the kernel density estimator based estimators of MI. However, because of issues with the behaviour of the kernel density estimators for finite sample size, we advocate the use of bootstrap based methods in determining the bias and standard error of such estimates. We perform some simulation studies to explore the finite sample behaviour of such MI estimates. We also develop MI-based tests to assess whether the components of the hybrid processes are independent and to compare the structure of multiple hybrid series. An application to a neuroscience data set is discussed.