We 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($\infty$), GARCH, ARCH($\infty$), 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 confirms the accuracy of this estimator.
"Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes." Electron. J. Statist. 11 (1) 452 - 479, 2017. https://doi.org/10.1214/17-EJS1241