Volume 6, 2002
New directions in Time Series Analysis (Guest Editor: Philippe Soulier)
|Page(s)||293 - 309|
|Section||New directions in Time Series Analysis (Guest Editor: Philippe Soulier)|
|Published online||15 November 2002|
Asymptotic behavior of the Empirical Process for Gaussian data presenting seasonal long-memory
Laboratoire de Statistique et Probabilités,
bâtiment M2, FRE 2222 du CNRS, Université des Sciences et Technologies de Lille,
59655 Villeneuve-d'Ascq Cedex, France; email@example.com.
We study the asymptotic behavior of the empirical process when the underlying data are Gaussian and exhibit seasonal long-memory. We prove that the limiting process can be quite different from the limit obtained in the case of regular long-memory. However, in both cases, the limiting process is degenerated. We apply our results to von–Mises functionals and U-Statistics.
Mathematics Subject Classification: 60G15 / 60G18 / 62G30 / 62M10
Key words: Empirical process / Hermite polynomials / Rosenblatt processes / seasonal long-memory / U-statistics von–Mises functionals.
© EDP Sciences, SMAI, 2002
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