In this Note, we study some general methods for testing the goodness-of-fit of a parametric model for a real-valued Markovian time series 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 Koul and Stute [1], and then widely developed by Ngatchou-Wandji [2,3] under more general conditions. Applications to general AR-ARCH models are given.
Dans cette note, nous étudions quelques méthodes générales pour tester un modèle paramétrique associé à une série chronologique markovienne à valeurs réelles lorsque les vecteurs aléatoires sont non stationnaires et absolument réguliers. Notre idée est d'utiliser un processus empirique marqué basé sur les résidus qui converge en loi vers un processus gaussien.
Accepted:
Published online:
Echarif Elharfaoui 1; Michel Harel 2, 3
@article{CRMATH_2016__354_10_1042_0,
author = {Echarif Elharfaoui and Michel Harel},
title = {A nonparametric model check for time series when the random vectors are nonstationary and absolutely regular},
journal = {Comptes Rendus. Math\'ematique},
pages = {1042--1047},
publisher = {Elsevier},
volume = {354},
number = {10},
year = {2016},
doi = {10.1016/j.crma.2016.07.014},
language = {en},
}
TY - JOUR AU - Echarif Elharfaoui AU - Michel Harel TI - A nonparametric model check for time series when the random vectors are nonstationary and absolutely regular JO - Comptes Rendus. Mathématique PY - 2016 SP - 1042 EP - 1047 VL - 354 IS - 10 PB - Elsevier DO - 10.1016/j.crma.2016.07.014 LA - en ID - CRMATH_2016__354_10_1042_0 ER -
%0 Journal Article %A Echarif Elharfaoui %A Michel Harel %T A nonparametric model check for time series when the random vectors are nonstationary and absolutely regular %J Comptes Rendus. Mathématique %D 2016 %P 1042-1047 %V 354 %N 10 %I Elsevier %R 10.1016/j.crma.2016.07.014 %G en %F CRMATH_2016__354_10_1042_0
Echarif Elharfaoui; Michel Harel. A nonparametric model check for time series when the random vectors are nonstationary and absolutely regular. Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 1042-1047. doi : 10.1016/j.crma.2016.07.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.07.014/
[1] Nonparametric model checks for time series, Ann. Stat., Volume 27 (1999), pp. 204-236
[2] Weak convergence of some marked empirical processes: application to testing heteroscedasticity, J. Nonparametr. Stat., Volume 14 (2002), pp. 325-339
[3] Local power of a Cramer–von Mises type test for parametric autoregressive models of order one, Comput. Math. Appl., Volume 56 (2008), pp. 918-929
[4] A Cramér–von Mises test for symmetry of the error distribution in asymptotically stationary stochastic models, Stat. Inference Stoch. Process., Volume 16 (2013), pp. 207-236
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