Maximum likelihood estimators of a long-memory process from discrete observations

Abstract

Abstract This paper deals with the problem of estimating the unknown parameters in a long-memory process based on the maximum likelihood method. The mean-square and the almost sure convergence of these estimators based on discrete-time observations are provided. Using Malliavin calculus, we present the asymptotic normality of these estimators. Simulation studies confirm the theoretical findings and show that the maximum likelihood technique can effectively reduce the mean-square error of our estimators.

Keywords

• Long-memory processes
• Maximum likelihood estimation
• Asymptotic analysis
• Malliavin calculus