Title: Testing hypotheses on the innovations distribution in GARCH-type models
Authors: Christian Francq - CREST and University Lille III (France)
Jean-Michel Zakoian - CREST (France) [presenting]
Abstract: Tests of different hypotheses in general GARCH models are proposed: adequacy of a parametric quantile, mean-median equality, symmetry of extreme quantiles and zero-median in presence of a conditional mean. The tests rely on the asymptotic distribution of the empirical distribution function of the residuals (edfr). For a large class of time series models (including the standard ARMA-GARCH),the asymptotic distribution of the edfr is impacted by the estimation but does not depend on the model parameters. The resulting tests are generally model-free (though not estimation-free) and thus are simple to implement. Efficiency comparisons are made using the Bahadur approach. A numerical study based on simulated and real data is provided.