A MINIMUM DISTANCE ESTIMATOR FOR LONG-MEMORY PROCESSES

This paper considers a minimum distance estimator (MDE) of the differe ncing parameter of the fractionally integrated white noise model. The MDE minimizes the difference between sample and population autocorrela tions. The paper presents calculations of asymptotic variances to exam ine the efficiency of the MDE relative to that of the MLE. For values of the differencing parameter less than 1/4, the MDE is root T-consist ent and asymptotically normal, and the asymptotic variance of the MDE using the first n autocorrelations approaches that of the MLE as n inc reases. However, there is a substantial efficiency loss if low-order a utocorrelations are omitted. This implies that a nonparametric treatme nt of short-run dynamics will involve a substantial loss of efficiency .