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Goodness-of-fit test for long range dependent processes

Published online by Cambridge University Press:  15 November 2002

Gilles Fay  and
Anne Philippe
Gilles Fay
Affiliation:
Laboratoire de Mathématiques Appliquées, FRE 2222 du CNRS, UFR de Mathématiques, bâtiment M2, Université des Sciences et Technologies de Lille, 59655 Villeneuve-d'Ascq Cedex, France; anne.philippe@univ-lille1.fr.
Anne Philippe
Affiliation:
Laboratoire de Mathématiques Appliquées, FRE 2222 du CNRS, UFR de Mathématiques, bâtiment M2, Université des Sciences et Technologies de Lille, 59655 Villeneuve-d'Ascq Cedex, France; anne.philippe@univ-lille1.fr.
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Abstract

In this paper, we make use of the information measure introduced by Mokkadem (1997) for building a goodness-of-fit test for long-range dependent processes. Our test statistic is performed in the frequency domain and writes as a non linear functional of the normalized periodogram. We establish the asymptotic distribution of our statistic under the null hypothesis. Under specific alternative hypotheses, we prove that the power converges to one. The performance of our test procedure is illustrated from different simulated series. In particular, we compare its size and its power with test of Chen and Deo.

Keywords

Goodness-of-fit test for spectral densityperiodogramlong range dependence.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 6: New directions in Time Series Analysis (Guest Editor: Philippe Soulier)New directions in Time Series Analysis (Guest Editor: Philippe Soulier) , 2002 , pp. 239 - 258
Copyright
© EDP Sciences, SMAI, 2002

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