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

This paper proposes some novel one-sided omnibus tests for independence between two multivariate stationary time series. These new apply the Hilbert-Schmidt criterion (HSIC) to test innovations of both Under regular conditions, limiting null distributions our HSIC-based are established. Next, shown be consistent. Moreover, a residual bootstrap method is used obtain critical values tests, and its validity justified. Compared with existing cross-correlation-based linear dependence, examine general (including non-linear) dependence give investigators more complete information on causal relationship The merits illustrated by simulation results real example.