ECF identification of GARCH systems driven by Lévy processes

Abstract: L\'evy processes are widely used in financial mathematics, telecommunication, economics, queueing theory and natural sciences for modelling. We propose an essentially asymptotically efficient estimation method for the system parameters of general autoregressive conditional heteroscedasticity (GARCH) processes. As an alternative to the maximum likelihood (ML) method we develop and analyze a novel identification method by adapting the so-called empirical characteristic function method (ECF) originally devised for estimating parameters of c.f.-s from i.i.d. samples. Precise characterization of the errors of these estimators will be given, and their asymptotic covariance matrices will be obtained.