TESTING FOR LONG MEMORY

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+