A minimum distance estimator for long-memory processes

This paper considers a minimum distance estimator (MDE) of the differencing parameter of the fractionally integrated white noise model. The MDE minimizes the difference between sample and population autocorrelations. The paper presents calculations of asymptotic variances to examine 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-consistent and asymptotically normal, and the asymptotic variance of the MDE using the first n autocorrelations approaches that of the MLE as n increases. However, there is a substantial efficiency loss if low-order autocorrelations are omitted. This implies that a nonparametric treatment of short-run dynamics will involve a substantial loss of efficiency.