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.

中文翻译：

---

用于两个平稳多元时间序列之间独立性的新的基于 HSIC 的测试

本文提出了一些新颖的单边综合检验，用于检验两个多元平稳时间序列之间的独立性。这些新测试应用希尔伯特-施密特独立性准则 (HSIC) 来测试两个时间序列创新之间的独立性。在常规条件下，我们建立了基于 HSIC 的测试的极限零分布。接下来，我们基于 HSIC 的测试被证明是一致的。此外，残差引导法用于获得我们基于 HSIC 的测试的临界值，其有效性是合理的。与现有的基于互相关的线性相关性测试相比，我们的测试检查了一般（包括线性和非线性）相关性，以便为研究人员提供关于两个多变量时间序列之间因果关系的更完整信息。