TESTING FOR LONG MEMORY

Abstract

This paper introduces a new test statistic for the null hypothesis of short memory against long memory alternatives. The novelty of our statistic is that it is based on only high-order sample autocovariances and by construction eliminates the effects of nuisance parameters typically induced by short memory autocorrelation. For practically relevant situations where the short memory process is not directly observed, but instead appears as the disturbance term in a deterministic linear regression model, we are able to demonstrate that our residual-based statistic has an asymptotic standard normal distribution under the null hypothesis. We also establish consistency of the statistic under long memory alternatives. The finite-sample properties of our procedure are compared to other well-known tests in the literature via Monte Carlo simulations. These show that the empirical size properties of the new statistic can be very robust compared to existing tests and also that it competes well in terms of power.We thank the associate editor and two anonymous referees for their valuable comments on an earlier draft of this paper.