On the sample mean of locally stationary long-memory processes

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.