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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 introducedby Mokkadem (1997) for building a goodness-of-fit test forlong-range dependent processes.Our test statistic is performed in the frequency domain and writes asa non linear functional of the normalized periodogram. We establishthe asymptotic distribution of our statistic under the nullhypothesis. Under specific alternative hypotheses, we prove that the powerconverges to one. The performance of our test procedure isillustrated from different simulated series. In particular,we compare its size and its power with test of Chenand Deo.

Keywords

Goodness-of-fit test for spectral densityperiodogramlong range dependence.

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