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Title: Testing the existence of moments and estimating the tail index of augmented GARCH processes Authors:  Christian Francq - CREST and University Lille III (France) [presenting]
Jean-Michel Zakoian - CREST (France)
Abstract: The purpose is to investigate the problem of testing finiteness of moments for a class of semi-parametric augmented GARCH(1,1) models encompassing the most commonly used GARCH-type specifications. The existence of positive-power moments of the strictly stationary solution is characterized through the Moment Generating Function (MGF) of the model, defined as the MGF of the logarithm of the random autoregressive coefficient in the volatility dynamics. We establish the asymptotic distribution of the empirical MGF, from which tests of moments are deduced. Alternative tests relying on the estimation of the maximal exponent characterizing the existence of moments are studied. The fully parametric case where the innovations density is either known or estimated is also considered. Power comparisons based on local alternatives and the Bahadur approach are proposed. Our results are illustrated via Monte Carlo experiments and real financial data.