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.
Accepted:
Published online:
Michel Harel 1, 2; Echarif Elharfaoui 1, 2
@article{CRMATH_2008__346_7-8_451_0,
author = {Michel Harel and Echarif Elharfaoui},
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},
journal = {Comptes Rendus. Math\'ematique},
pages = {451--455},
publisher = {Elsevier},
volume = {346},
number = {7-8},
year = {2008},
doi = {10.1016/j.crma.2008.02.018},
language = {en},
}
TY - JOUR AU - Michel Harel AU - Echarif Elharfaoui TI - 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 JO - Comptes Rendus. Mathématique PY - 2008 SP - 451 EP - 455 VL - 346 IS - 7-8 PB - Elsevier DO - 10.1016/j.crma.2008.02.018 LA - en ID - CRMATH_2008__346_7-8_451_0 ER -
%0 Journal Article %A Michel Harel %A Echarif Elharfaoui %T 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 %J Comptes Rendus. Mathématique %D 2008 %P 451-455 %V 346 %N 7-8 %I Elsevier %R 10.1016/j.crma.2008.02.018 %G en %F CRMATH_2008__346_7-8_451_0
Michel Harel; Echarif Elharfaoui. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.02.018/
[1] Weak convergence of some marked empirical processes: Application to testing heteroscedasticity, J. Nonparametr. Statist., Volume 14 (2002), pp. 325-339
[2] 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] Nonparametric model checks for regression, Ann. Statist., Volume 25 (1997), pp. 613-641
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