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

We study the problem of parameter estimation for Ornstein–Uhlenbeck processes driven by symmetric α-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 α-stable motions (0 > α > 2) than for the process driven by the classical Gaussian case (α = 2). Copyright The Institute of Statistical Mathematics, Tokyo 2013