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

Miklos Csorgo, Barbara Szyszkowicz and Lihong Wang
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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

No lrsp-TRS387, RePAd Working Paper Series from Département des sciences administratives, UQO

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.

Keywords: Long-range dependence; Sequential empirical and quantile processes; Sequential Bahadur-Kiefer process; Sequential Vervaat and Vervaat error processes; Strong invariance principles. (search for similar items in EconPapers)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Date: Written 2000-01-01
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