New HSIC-based tests for independence between two stationary multivariate time series
Abstract
This paper proposes some novel one-sided omnibus tests for independence between two multivariate stationary time series. These new tests apply the Hilbert-Schmidt independence criterion (HSIC) to test the independence between the innovations of both time series. Under regular conditions, the limiting null distributions of our HSIC-based tests are established. Next, our HSIC-based tests are shown to be consistent. Moreover, a residual bootstrap method is used to obtain the critical values for our HSIC-based tests, and its validity is justified. Compared with the existing cross-correlation-based tests for linear dependence, our tests examine the general (including both linear and non-linear) dependence to give investigators more complete information on the causal relationship between two multivariate time series. The merits of our tests are illustrated by some simulation results and a real example.
Cite
@article{arxiv.1804.09866,
title = {New HSIC-based tests for independence between two stationary multivariate time series},
author = {Guochang Wang and Wai Keung Li and Ke Zhu},
journal= {arXiv preprint arXiv:1804.09866},
year = {2018}
}