LIMITING DISTRIBUTION OF WEIGHTED PROCESSES OF RESIDUALS - APPLICATION TO PARAMETRIC NONLINEAR AUTOREGRESSIVE MODELS

We introduce methods for testing the goodness-of-fit of linear or nonl inear parametric autoregressive models of order 1, under stationarity and ergodicity assumptions. We establish two functional limit theorems for the process of deviations (A) over cap n(.) between the weighted process of residuals under consideration and its parametric counterpar t, under the null hypothesis H-0. We discuss several possible tests ba sed on these results and show that the half-sample method introduced b y [10] for parametric distribution function models can be adapted to t he present setting.