# Adaptive estimator of the memory parameter and goodness-of-fit test using a multidimensional increment ratio statistic

Abstract : The increment ratio (IR) statistic was first defined and studied in Surgailis {\it et al.} (2007) for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in the case of stationary processes. Firstly, a multidimensional central limit theorem is established for a vector composed by several IR statistics. Secondly, a goodness-of-fit $\chi^2$-type test can be deduced from this theorem. Finally, this theorem allows to construct adaptive versions of the estimator and test which are studied in a general semiparametric frame. The adaptive estimator of the long-memory parameter is proved to follow an oracle property. Simulations attest of the interesting accuracies and robustness of the estimator and test, even in the non Gaussian case.
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Article dans une revue
Journal of Multivariate Analysis, Elsevier, 2012, pp.222-240
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https://hal.archives-ouvertes.fr/hal-00522842
Contributeur : Jean-Marc Bardet <>
Soumis le : jeudi 22 septembre 2011 - 09:12:06
Dernière modification le : mardi 26 février 2013 - 19:56:42
Document(s) archivé(s) le : vendredi 23 décembre 2011 - 02:21:46

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• HAL Id : hal-00522842, version 2
• ARXIV : 1010.0426

### Citation

Jean-Marc Bardet, Béchir Dola. Adaptive estimator of the memory parameter and goodness-of-fit test using a multidimensional increment ratio statistic. Journal of Multivariate Analysis, Elsevier, 2012, pp.222-240. 〈hal-00522842v2〉

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