  We propose generalized portmanteau-type test statistics in the frequency
domain to test independence between two stationary time series. The test
statistics are formed analogous to the one in Chen and Deo (2004, Econometric
Theory 20, 382-416), who extended the applicability of portmanteau
goodness-of-fit test to the long memory case. Under the null hypothesis of
independence, the asymptotic standard normal distributions of the proposed
statistics are derived under fairly mild conditions. In particular, each time
series is allowed to possess short memory, long memory or anti-persistence. A
simulation study shows that the tests have reasonable size and power
properties.
