A NONPARAMETRIC TEST FOR GENERALIZED FIRST-ORDER AUTOREGRESSIVE MODELS

We derive a non-parametric test for testing the presence of V(X-i, eps ilon(i)) in the non-parametric first-order autoregressive model Xi+) = T(X-i) + V(X-i, epsilon(i)) + U(X-i)epsilon(i+1), where the function T(x) is assumed known. The test is constructed as a functional of a ba sic process for which we establish a weak invariance principle, under the null hypothesis and under stationarity and mixing assumptions. Bou nds for the local and non-local powers are provided under a condition which ensures that the power tends to one as the sample size tends to infinity. The testing procedure can be applied, e.g. to bilinear model s, ARCH models, EXPAR models and to some other uncommon models. Our re sults confirm the robustness of the test constructed in Ngatchou Wandj i (1995) and in Diebolt & Ngatchou Wandji (1995).