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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 asymptotic 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-00002192
Contributor : Pierre Lafaye de Micheaux <>
Submitted on : Monday, December 23, 2002 - 2:42:37 AM
Last modification on : Wednesday, October 11, 2017 - 1:03:34 AM
Long-term archiving on: : Tuesday, September 11, 2012 - 7:10:25 PM

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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-00002192⟩

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