A least squares estimator for discretely observed Ornstein-Uhlenbeck processes driven by symmetric alpha-stable motions

作者：Zhang, Shibin^*; Zhang, Xinsheng

来源：Annals of the Institute of Statistical Mathematics, 2013, 65(1): 89-103.

DOI：10.1007/s10463-012-0362-0

• Stable law
• Ornstein-Uhlenbeck
• Parametric estimation
• Consistency
• Asymptotic distribution
• Least squares method

We study the problem of parameter estimation for Ornstein-Uhlenbeck processes driven by symmetric alpha-stable motions, based on discrete observations. A least squares estimator is obtained by minimizing a contrast function based on the integral form of the process. Let h be the length of time interval between two consecutive observations. For both the case of fixed h and that of h -> 0, consistencies and asymptotic distributions of the estimator are derived. Moreover, for both of the cases of h, the estimator has a higher order of convergence for the Ornstein-Uhlenbeck process driven by non-Gaussian alpha-stable motions (0 < alpha < 2) than for the process driven by the classical Gaussian case (alpha = 2).

• 出版日期2013-2
• 单位复旦大学; 上海海事大学