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

摘要

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.