There exist several estimators of the memory parameter in long-memory time series models with mean µ and the spectrum specified only locally near zero frequency. In this paper we give a lower bound for the rate of convergence of any estimator of the memory parameter as a function of the degree...

In Giraitis, Robinson, and Samarov (1997), we have shown that the optimal rate for memory parameter estimators in semiparametric long memory models with degree of "local smoothness" [beta] is n-r([beta]), r([beta])=[beta]/(2[beta]+1), and that a log-periodogram regression estimator (a modified...