On estimating the self similarity index for a long range dependent process

Research Report SRR95-032

On estimating the self similarity index for a long range dependent process

Peter Hall, Hira L. Koul, Berwin A. Turlach

Abstract: This paper develops estimators of the dependence parameter, or self-similarity index, of a long-range dependent time series that need not be Gaussian. Unlike many predecessors, our estimators are based directly on sample auto-covariances rather than on the spectral density. Our approach is semiparametric, in that the slowly varying portion of the autocovariance function need not be known. We derive explicit convergence rates, which are shown to be near the best possible for these types of estimators. Our results elucidate an important recent contribution of Robinson (1994), who showed that consistent estimation is possible but did not provide explicit rates.

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