A Large Sample Independence Test for Finite Mean Processes

We use the sample covariation to develop asymptotic tests for independence for data in the normal domain of attraction of a stable law. The tests can be used for finite or infinite variance processes. In a simulation study we compare the finite sample performance of the proposed tests to the Portmanteau test commonly used in time series modeling. The null convergence of the test statistics to their asymptotic distribution seems to be faster than that of the Portmanteau statistic, especially when the data is fat-tailed. In the finite variance case, the proposed tests have the same asymptotic power properties as the Portmanteau test and have similar small sample empirical power. Simulations indicate the covariation test has a higher power for small sample sizes when the process is symmetric stable with tail decay parameter .