Testing That a Dependent Process Is Uncorrelated

An analysis is presented of a new testing procedure for the null hypothesis that a stochastic process is uncorrelated when the process is possibly dependent. Unlike with existing procedures, the user does not need to choose any arbitrary number to implement the proposed test. The asymptotic null distribution of the proposed test statistic is not standard, but it is tabulated by means of simulations. The test is compared with two alternative test procedures that require selection of user-chosen numbers on the basis of asymptotic local power and finite sample behavior. Although the asymptotic local power of the proposed test is lower than those corresponding to the alternative tests, in a Monte Carlo study I show that in small samples the test typically better controls the type I error and that the loss of power is not substantial.