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Title: Almost sure convergence of the Bartlett estimator
Authors: Berkes, I.
Horváth, L.
Kokoszka, P.
Shao, Q.-M. 
Keywords: Cumulants
Increments of partial sums
Long-range dependence
Variance of the mean
Weak dependence
Issue Date: Nov-2005
Citation: Berkes, I.,Horváth, L.,Kokoszka, P.,Shao, Q.-M. (2005-11). Almost sure convergence of the Bartlett estimator. Periodica Mathematica Hungarica 51 (1) : 11-25. ScholarBank@NUS Repository.
Abstract: We study the almost sure convergence of the Bartlett estimator for the asymptotic variance of the sample mean of a stationary weekly dependent process. We also study the a.\ s.\ behavior of this estimator in the case of long-range dependent observations. In the weakly dependent case, we establish conditions under which the estimator is strongly consistent. We also show that, after appropriate normalization, the estimator converges a.s. in the long-range dependent case as well. In both cases, our conditions involve fourth order cumulants and assumptions on the rate of growth of the truncation parameter appearing in the definition of the Bartlett estimator. © Akadémiai Kiadó.
Source Title: Periodica Mathematica Hungarica
ISSN: 00315303
DOI: 10.1007/s10998-005-0017-5
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