NEW HSIC-BASED TESTS FOR INDEPENDENCE BETWEEN TWO STATIONARY MULTIVARIATE TIME SERIES

We propose 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 the time series. We establish the limiting null distributions of our HSIC-based tests under regular conditions. Next, our HSIC-based tests are shown to be consistent. A residual bootstrap method is used to obtain the critical values for the tests, and its validity is justified. Existing cross-correlation-based tests examine linear dependence. In contrast, our tests examine general dependence (including linear and non-linear), providing researchers with information that is more complete on the causal relationship between two multivariate time series. The merits of our tests are illustrated using simulations and a real-data example.

Automated summary

This study introduces novel one-sided omnibus tests for independence between two multivariate stationary time series, utilizing the Hilbert-Schmidt independence criterion (HSIC) to analyze the independence between the innovations of the time series. The study establishes the limiting null distributions of the tests under regular conditions and demonstrates the consistency of the HSIC-based tests. The use of a residual bootstrap method for obtaining critical values and the examination of general dependence in contrast to existing linear cross-correlation tests are highlighted as the key contributions of this research.