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On bootstrapping periodic random arrays with increasing period

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Abstract

The aim of the paper is to determine when the periodic block bootstrap, procedure introduced by Chan et al. (Technometrics 46(2):215–224, 2004), can be applied to arrays of random variables. Formal consistency is obtained under α-mixing or m-dependence conditions together with the assumption that the length of the period tends to infinity. On the other hand, if the period is constant, inconsistency is shown. The performance of periodic block bootstrap is also compared in simulations with moving block bootstrap. It is suggested that for the case of long-period data the first method is more effective and much more stable with respect to the length of the block size.

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Authors and Affiliations

  1. Department of Econometrics, The Graduate School of Business WSB-NLU, ul. Zielona 27, 33-300, Nowy Sacz, Poland

    Jacek Leśkow

  2. Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059, Krakow, Poland

    Rafał Synowiecki

Authors
  1. Jacek Leśkow
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  2. Rafał Synowiecki
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Correspondence to Rafał Synowiecki.

Additional information

Work partially supported by the following grants: NATO Collaborative Linkage Grant no. ICS.NUKR.CLG 983335, AGH local grant no. 10.420.03, EC FP6 Marie Curie ToK programme SPADE-2 at IMPAN, Warsaw.

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Leśkow, J., Synowiecki, R. On bootstrapping periodic random arrays with increasing period. Metrika 71, 253–279 (2010). https://doi.org/10.1007/s00184-008-0228-x

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  • DOI: https://doi.org/10.1007/s00184-008-0228-x

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