Standard Laplace quasi-maximum likelihood estimator for GARCH processes

We propose a consistent estimator for the noise mean m of the GARCH process based on Laplace (m,1) errors. Also, we prove the consistency and asymptotic normality for the Quasi-Maximum Likelihood Estimator of the GARCH model based on the Laplace residuals with any mean value for the residuals. Numerical simulations confirm the accuracy of the estimators.

Automated summary

This paper proposes a consistent estimator for the noise mean of the GARCH process based on Laplace errors. It also proves the consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator of the GARCH model based on Laplace residuals with any mean value. Numerical simulations confirm the accuracy of the estimators.