On the sample mean of locally stationary long-memory processes

Abstract

Some asymptotic statistical properties of the sample mean of a class locally stationary long-memory process are studied in this paper. Conditions for consistency are investigated and precise convergence rates of the variance of the sample mean are established for a class of time-varying long-memory parameter functions. A central limit theorem for the sample mean is also established. Furthermore, the calculation of the variance of the sample mean is illustrated through several numerical and simulation experiments. (C) 2010 Elsevier B.V. All rights reserved.