Adaptive semiparametric wavelet estimator and goodness-of-fit test for long memory linear processes

Jean-Marc Bardet (1) , Hatem Bibi (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

This paper is first devoted to study an adaptive wavelet based estimator of the long memory parameter for linear processes in a general semi-parametric frame. This is an extension of Bardet {\it et al.} (2008) which only concerned Gaussian processes. Moreover, the definition of the long memory parameter estimator is modified and asymptotic results are improved even in the Gaussian case. Finally an adaptive goodness-of-fit test is also built and easy to be employed: it is a chi-square type test. Simulations confirm the interesting properties of consistency and robustness of the adaptive estimator and test.

Mots clés: adaptive goodness-of-fit test; Long range dependence; linear processes; wavelet estimator; semiparametric estimator; adaptive estimator; adaptive goodness-of-fit test.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Marc Bardet, Hatem Bibi. Adaptive semiparametric wavelet estimator and goodness-of-fit test for long memory linear processes. Electronic Journal of Statistics , 2012, 6, pp.2382-2419. ⟨hal-00542325⟩