The decomposition and measurement of the interdependency between second-order stationary processes

Abstract

For a given pair of multivariate stationary processes, the process of one-way effect is extracted from each of the processes. Each process is decomposed into two orthogonal processes, namely, into the process generated by the one-way effect of the other process and the process orthogonal to it. Based on the decomposition, three measures characterizing the interdependency of the pair of processes are introduced. They are the measure of association, the measure of one-way effect and the measure of reciprocity. Each of the measures is defined as overall as well as frequencywise measure. The paper shows that the measure of association is equal to the sum of the others. It discusses the relationships of those measures to the ones proposed by Gel'fand-Yaglom and by Geweke.