Estimating the mean under strong persistence

摘要

We study a maximum likelihood [ML] type estimator for the mean of strongly persistent processes. Its limiting Gaussian distribution is obtained and compared with that of the arithmetic sample mean. The rates of convergence turn out to be equal. Two special cases of strong persistence are discussed: Fractional integration [FI] and harmonic weighting [HW]. Notwithstanding equal rates, efficiency gains relative to the arithmetic mean are available under FI, while for HW processes the relative efficiency turns out to be one asymptotically. For applied work, where the true model is not known, we suggest to use the estimator building on HW as a general purpose device, since it does not require the estimation of any parameter. (C) 2020 Elsevier B.V. All rights reserved.