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Goodness-of-fit tests in long-range dependent processes under fixed alternatives

Published online by Cambridge University Press:  21 May 2013

Holger Dette  and
Kemal Sen
Holger Dette
Affiliation:
Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany. holger.dette@ruhr-uni-bochum.de; kemal.sen@ruhr-uni-bochum.de
Kemal Sen
Affiliation:
Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany. holger.dette@ruhr-uni-bochum.de; kemal.sen@ruhr-uni-bochum.de
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Abstract

In a recent paper Fay and Philippe [ESAIM: PS 6 (2002) 239–258] proposed a goodness-of-fit test for long-range dependent processes which uses the logarithmic contrast as information measure. These authors established asymptotic normality under the null hypothesis and local alternatives. In the present note we extend these results and show that the corresponding test statistic is also normally distributed under fixed alternatives.

Keywords

Long-range dependencegoodness-of-fit testasymptotic powerperiodogram
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 17 , 2013 , pp. 432 - 443
Copyright
© EDP Sciences, SMAI, 2013

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