Generalized moment estimators for $$\alpha $$-stable Ornstein–Uhlenbeck motions from discrete observations

Abstract

We study the parameter estimation problem for discretely observed Ornstein–Uhlenbeck processes driven by $$\alpha $$-stable Levy motions. A method of moments via ergodic theory and via sample characteristic functions is proposed to estimate all the parameters involved in the Ornstein–Uhlenbeck processes. We obtain the strong consistency and asymptotic normality of the proposed joint estimators when the sample size $$n \rightarrow \infty $$ while the sampling time step h remains arbitrarily fixed. We also design a procedure to select the grid points in the characteristic functions in certain optimal way for the proposed estimators.