title: Rate Optimal Semiparametric Estimationof the Memory Parameter of the Gaussian Time Series with Long Range Dependence
creator: Giraitis, Liudas
creator: Robinson, Peter M.
creator: Samarov, Alexander
subject: ddc-510
subject: 510 Mathematics
description: 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.
date: 1995-05
type: Working paper
type: info:eu-repo/semantics/workingPaper
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/20900/1/beitrag.28.pdf
identifier: DOI:10.11588/heidok.00020900
identifier: urn:nbn:de:bsz:16-heidok-209007
identifier:   Giraitis, Liudas ; Robinson, Peter M. ; Samarov, Alexander  (1995) Rate Optimal Semiparametric Estimationof the Memory Parameter of the Gaussian Time Series with Long Range Dependence.  [Working paper]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/20900/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng