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Rate Optimal Semiparametric Estimationof the Memory Parameter of the Gaussian Time Series with Long Range Dependence

Giraitis, Liudas ; Robinson, Peter M. ; Samarov, Alexander

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Abstract

There exist several estimators of the memory parameter in long-memorytime series models with mean mu and the spectrum specified only locally near zerofrequency. In this paper we give a lower bound for the rate of convergence of anyestimator of the memory parameter as a function of the degree of local smoothnessof the spectral density at zero. The lower bound allows one to evaluate andcompare different estimators by their asymptotic behavior, and to claim the rateoptimality for any estimator attaining the bound. A log-periodogram regressionestimator, analysed by Robinson (1992), is then shown to attain the lower bound,and is thus rate optimal.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 09 Jun 2016 08:54
Date: May 1995
Number of Pages: 12
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
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