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

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. To cite this article: M. Harel, E. Elharfaoui, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

RésuméNous 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. Pour citer cet article : M. Harel, E. Elharfaoui, C. R. Acad. Sci. Paris, Ser. I 346 (2008).