Goodness-of-fit test for long range dependent processes
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;
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.
Mathematics Subject Classification: 60F05 / 62F03
Key words: Goodness-of-fit test for spectral density / periodogram / long range dependence.
© EDP Sciences, SMAI, 2002