Numerical estimation of log-GARCH model with relaxed moment assumptions

Abstract

Abstract This paper provides algorithms for the numerical estimation of the log-GARCH model parameters with no assumptions on the existence of the log-moment orders greater than one. Our approach is based on the quasi-maximum likelihood estimation combined with the information filter. The proposed estimation is employed for two aims. The first is to treat the zero returns considered as missing values through an EM imputation algorithm. The second is to compute the kurtosis of the log-GARCH process by the so-called, right and left measures. A Monte Carlo simulation is performed to investigate the potential of the proposed algorithms to improve the accuracy of the quasi-maximum likelihood for the parameter estimation and the treatment of zero returns as well as to check the robustness of the used kurtosis measures.