Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of a ne causal processes

Abstract

AbstractWe prove the consistency and asymptotic normality of the Laplacian Quasi-Maximum Likelihood Estimator (QMLE) for a general class of causal time series including ARMA, AR(1), GARCH, ARCH(1), ARMA-GARCH, APARCH, ARMA-APARCH,..., processes. We notably exhibit the advantages (moment order and robustness) of this estimator compared to the classical Gaussian QMLE. Numerical simulations con rms the accuracy of this estimator.