Goodness-of-fit test for long range dependent processes
ESAIM: Probability and Statistics, Tome 6 (2002), pp. 239-258.

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.

DOI : 10.1051/ps:2002013
Classification : 60F05, 62F03
Mots clés : goodness-of-fit test for spectral density, periodogram, long range dependence 
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Fay, Gilles; Philippe, Anne. Goodness-of-fit test for long range dependent processes. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 239-258. doi : 10.1051/ps:2002013. http://www.numdam.org/articles/10.1051/ps:2002013/

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