Distance covariance for stochastic processes
Matsui, Muneya; Mikosch, Thomas; Samorodnitsky, Gennady
The distance covariance of two random vectors is a measure of their dependence. The empirical distance covariance and correlation can be used as statistical tools for testing whether two random vectors are independent. We propose an analogs of the distance covariance for two stochastic processes defined on some interval. Their empirical analogs can be used to test the independence of two processes.
Muneya Matsui's research is partly supported by JSPS Grant-in-Aid for Young Scientists B (16K16023) and Nanzan University Pache Research Subsidy I-A-2 for the 2016 academic year. Thomas Mikosch's research is partly supported by the Danish Research Council Grant DFF-4002-00435. Gennady Samorodnitsky's research is partly supported by the ARO MURI grant W911NF-12-1-0385.
emnpirical characteristic function, distance covariance, stochastic process, test of independence