Statistics/Probability Theory
The marked empirical process to test a general AR-ARCH against an other general AR-ARCH when the random vectors are nonstationary and absolutely regular
Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 451-455.

In this Note, we study a procedure on goodness-of-fit testing for nonlinear time-series models against a large class of alternatives under nonstationarity and absolute regularity. For that, we define a marked empirical process based on residuals which converges in distribution to a Gaussian process with respect to the Skorohod topology. This method was first introduced by Stute (1997) and then widely developed by Ngatchou-Wandji (2002, 2005, 2008) [1–3] under more general conditions. Applications to general AR-ARCH models are given.

Nous étudions une procédure pour tester des modèles de régression non stationnaires et absolument réguliers contre une large classe d'alternatives. Notre idée est d'utiliser un processus empirique marqué basé sur les résidus qui converge en loi vers un processus gaussien.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.02.018
Harel, Michel 1, 2; Elharfaoui, Echarif 1, 2

1 LSP U.M.R. 5219 CNRS, 31062 Toulouse cedex 9, France
2 IUFM du Limousin, 209, boulevard de Vanteaux, 87036 Limoges cedex, France
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     title = {The marked empirical process to test a general {AR-ARCH} against an other general {AR-ARCH} when the random vectors are nonstationary and absolutely regular},
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Harel, Michel; Elharfaoui, Echarif. The marked empirical process to test a general AR-ARCH against an other general AR-ARCH when the random vectors are nonstationary and absolutely regular. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 451-455. doi : 10.1016/j.crma.2008.02.018. http://www.numdam.org/articles/10.1016/j.crma.2008.02.018/

[1] Ngatchou-Wandji, J. Weak convergence of some marked empirical processes: Application to testing heteroscedasticity, J. Nonparametr. Statist., Volume 14 (2002), pp. 325-339

[2] Ngatchou-Wandji, J. Checking nonlinear heteroscedastic time series models, J. Statist. Plann. Inference, Volume 133 (2005), pp. 33-68

[3] J. Ngatchou-Wandji, N. Laîb, Local power of a Cramer–von Mises type test for parametric autoregressive models of order one, Comput. Math. Apll. (2008), in press

[4] Stute, W. Nonparametric model checks for regression, Ann. Statist., Volume 25 (1997), pp. 613-641

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