Parameter Estimations for Skew Ornstein-Uhlenbeck Processes

Ailing Feng

Abstract: In this paper, we study the parameter estimations for the skew Ornstein-Uhlenbeck processes based on continuous observations. However, dealing with the skew Ornstein-Uhlenbeck processes are tough because of the appearance of the local time. Therefore, we transform the skew Ornstein-Uhlenbeck processes into the standard diffusion processes, and then utilize the measure transformation to obtain the log likelihood function. At the same time we derive the formulas for the estimators of the drift parameter. Furthermore, we prove their consistency and asymptotic normality.

Keywords: Parameter estimation, Skew Ornstein-Uhlenbeck process, The log likelihood function, Strong consistency, Asymptotic normality