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Strong invariance principles for sequential Bahadur-Kiefer and Vervaat error processes of long-range dependent sequences

Author

Listed:
  • Miklos Csorgo

    (School of Mathematics and Statistics, Carleton University)

  • Barbara Szyszkowicz

    (School of Mathematics and Statistics, Carleton University)

  • Lihong Wang

    (Department of Mathematics, Nanjing University)

Abstract

In this paper we study strong approximations (invariance principles) of the sequential uniform and general Bahadur-Kiefer processes of long-range dependent sequences. We also investigate the strong and weak asymptotic behavior of the sequential Vervaat process, i.e., the integrated sequential Bahadur-Kiefer process, properly normalized, as well as that of its deviation from its limiting process, the so-called Vervaat error process. It is well known that the Bahadur-Kiefer and the Vervaat error processes cannot converge weakly in the i.i.d. case. In contrast to this we conclude that the Bahadur-Kiefer and Vervaat error processes, as well as their sequential versions, do converge weakly to a Dehling-Taqqu type limit process for certain long-range dependent sequences.

Suggested Citation

  • Miklos Csorgo & Barbara Szyszkowicz & Lihong Wang, 2000. "Strong invariance principles for sequential Bahadur-Kiefer and Vervaat error processes of long-range dependent sequences," RePAd Working Paper Series lrsp-TRS387, Département des sciences administratives, UQO.
    • Handle: RePEc:pqs:wpaper:0152005
    as

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    File URL: http://www.repad.org/ca/on/lrsp/TRS387.pdf
    File Function: First version, 2000
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    References listed on IDEAS

    as
    1. Csörgo, Miklós & Zitikis, Ricardas, 2001. "The Vervaat Process in Lp Spaces," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 103-138, July.
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    More about this item

    Keywords

    Long-range dependence; Sequential empirical and quantile processes; Sequential Bahadur-Kiefer process; Sequential Vervaat and Vervaat error processes; Strong invariance principles.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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