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Rate optimal semiparametric estimation of the memory parameter of the Gaussian time series with long-range dependence

Giraitis, Liudas, Robinson, Peter M. and Samarov, Alexander (1997) Rate optimal semiparametric estimation of the memory parameter of the Gaussian time series with long-range dependence. Econometrics; EM/1997/323, EM/1997/323. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.

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Abstract

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 of local smoothness of the spectral density at zero. The lower bound allows one to evaluate and compare different estimators by their asymptotic behaviour, and to claim the rate optimality for any estimator attaining the bound. The log-periodogram regression estimator, analysed by Robinson (1992), is then shown to attain the lower bound, and is thus rate optimal.

Item Type: Monograph (Discussion Paper)
Official URL: http://sticerd.lse.ac.uk
Additional Information: © 1997 the authors
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Sets: Collections > Economists Online
Departments > Economics
Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: EM/1997/323
Date Deposited: 27 Apr 2007
URL: http://eprints.lse.ac.uk/2175/

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