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. Copyright © 2021 Institute of Statistical Science, Academia Sinica.
|Publication status||Published - Jan 2021|
CitationWang, G., Li, W. K., & Zhu, K. (2021). New HSIC-based tests for independence between two stationary multivariate time series. Statistica Sinica, 31(1), 269-300.
- Hilbert-Schmidt independence criterion
- Multivariate time series models
- Non-linear dependence
- Residual bootstrap
- Testing for independence