Note on convergence rates of semiparametric estimators of dependence index

Abstract

Considerable recent attention has been devoted to semiparametric estimation of the dependence index, or the Hurst constant, using methods based on information in either frequency or time domains. Convergence rates of estimators in the frequency domain have been derived, and in the present paper we obtain them for estimators in the time domain. It is shown that the latter can have superior performance for moderate-range time series, but are inferior in the context of long-range dependence.