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Almost sure convergence of the Bartlett estimator

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Summary

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.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, A. Rényi Institute of Mathematics Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest Hungary, Budapest

    István Berkes

  2. Department of Mathematics University of Utah, 155 South 1440 East Salt Lake City, UT 84112-0090 USA

    Lajos Horváth

  3. Department of Mathematics and Statistics Utah State University, 3900 Old Main Hill Logan, UT 84322-3900 USA

    Piotr Kokoszka

  4. Department of Mathematics University of Oregon, Eugene, OR 97403-1222\ USA

    Qi-man Shao

Authors
  1. István Berkes
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  2. Lajos Horváth
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  3. Piotr Kokoszka
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  4. Qi-man Shao
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Berkes, I., Horváth, L., Kokoszka, P. et al. Almost sure convergence of the Bartlett estimator. Period Math Hung 51, 11–25 (2005). https://doi.org/10.1007/s10998-005-0017-5

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  • DOI: https://doi.org/10.1007/s10998-005-0017-5

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