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

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.MSC: Primary 62D05; secondary 62J12

Parameter estimation for discretized geometric fractional Brownian motions with applications in Chinese financial markets

“…As a consequence, parameter estimation for gfBm as a challenging theoretical problem has been of great interest in the past decade. For example, the problem of parameter estimation in a simple linear model driven by a fBm was investigated in Bertin et al [5], Bertin et al [6], Hu et al [21], Xiao et al [41], Brouste and Iacus [7], Liu and Song [27], Xiao et al [42], Cheng et al [9], Xiao et al [46], Sun et al [37]. In ground-breaking works, Xiao et al [44], Xiao et al [45], Tanaka et al [38], Wang et al [39] established the asymptotic theory for the estimators of fractional Ornstein-Uhlenbeck processes.…”