标题： 基于HSIC的两种平稳多变量时间序列之间独立性的检验 显示英文标题

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

摘要： 本文提出了一些新的单边整体检验方法，用于检验两个多变量平稳时间序列之间的独立性。这些新检验方法将希尔伯特-施密特独立准则（HSIC）应用于两个时间序列的创新项之间的独立性检验。在常规条件下，我们建立了基于HSIC的检验的极限零分布。接下来，我们的基于HSIC的检验被证明是一致的。此外，使用残差引导方法来获得基于HSIC的检验的临界值，并验证了其有效性。与现有的基于交叉相关性的线性依赖检验相比，我们的检验可以检验一般的（包括线性和非线性）依赖关系，从而为研究者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。我们的检验的优点通过一些模拟结果和一个实际例子进行了说明。 显示英文摘要

摘要： 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.