Asymptotic properties for the parameter estimation in Ornstein-Uhlenbeck process with discrete observations

Abstract

In this paper, under discrete observations, we study Cramér-type moderate deviations (extended central limit theorem) for parameter estimation in Ornstein-Uhlenbeck process. Our results contain both stationary and explosive cases. For applications, we propose test statistics which can be used to construct rejection regions in the hypothesis testing for the drift coefficient, and the corresponding probability of type II error tends to zero exponentially. Simulation study shows that our test statistics have good finite-sample performances both in size and power. The main methods include the deviation inequalities for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques.