Résumé : It is generally admitted that financial time series have heavy tailed marginal distributions. When time series models are fitted on such data, the non-existence of appropriate moments may invalidate standard statistical tools used for inference. Moreover, the existence of moments can be crucial for risk management. This talk considers testing the existence of moments in the framework of standard and augmented GARCH models. In the case of standard GARCH, even-moment conditions involve moments of the independent innovation process. We propose tests for the existence of moments of the returns process that are based on the joint asymptotic distribution of the estimator of the volatility parameters and empirical moments of the residuals. To achieve efficiency gains we consider non Gaussian QML estimators founded on reparametrizations of the GARCH model, and we discuss optimality issues. We also consider augmented GARCH processes, for which moment conditions are less explicit. We establish the asymptotic distribution of the empirical moment Generating function (MGF) of the model, defined as the MGF of the random autoregressive coefficient in the volatility dynamics, from which a test is deduced. An alternative test is based on the estimation of the maximal exponent characterizing the existence of moments. Our results will be illustrated with Monte Carlo experiments and real financial data.

Keywords : conditional variance models; tests of moments; efficiency comparisons