# New HSIC-based tests for independence between two stationary multivariate time series

arXiv: https://arxiv.org/abs/1804.09866 · HTML: https://mlsanity.com/paper/1804.09866/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Explaining Categorical Feature Interactions Using Graph Covariance and LLMs](https://mlsanity.com/paper/2501.14932/) (2025)

## Abstract (arXiv)

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.