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Tests d'indépendance en analyse multivariée et tests de normalité dans les modèles ARMA

Abstract : We build a goodness-of-fit test of normality for the innovations of an ARMA( p,q ) model with known mean or trend. This test is based on the data driven smooth test approach and is simple to perform. An extensive simulation study is conducted to study the behavior of the test for moderate sample sizes. Our approach is generally more powerful than existing tests while holding its level throughout most of the parameter space. This agrees with theoretical results showing the superiority of the data driven smooth test approach in related contexts. A semi-parametric test of independence (or serial independence) is proposed between marginal vectors each of which is normally distributed but without assuming the joint normality of these marginal vectors. The test statistic is a Cramér-von Mises functional of a process defined from the empirical characteristic function. This process is defined similarly as the process of Ghoudi et al. (2001) built from the empirical distribution function and used to test for independence between univariate marginal variables. The test statistic can be represented as a V statistic. It is consistent to detect any form of dependence. The weak convergence of the process is derived. The asymp- totic distribution of the Cramér-von Mises functionals is approximated by the Cornish-Fisher expansion using a recursive formula for cumulants and by the numerical evaluations of the eigenvalues in the inversion formula. The test statistic is finally compared with Wilks' statistic for testing the parametric hypothesis of independence in the one-way MANOVA model with random effects.
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https://tel.archives-ouvertes.fr/tel-00299325
Contributor : Pierre Lafaye de Micheaux <>
Submitted on : Thursday, July 17, 2008 - 11:04:11 AM
Last modification on : Monday, August 31, 2020 - 4:22:04 PM
Long-term archiving on: : Monday, May 31, 2010 - 8:30:23 PM

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  • HAL Id : tel-00299325, version 1

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Pierre Lafaye de Micheaux. Tests d'indépendance en analyse multivariée et tests de normalité dans les modèles ARMA. Mathématiques [math]. Université Montpellier II - Sciences et Techniques du Languedoc, 2002. Français. ⟨tel-00299325⟩

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