Cramér-type moderate deviations for statistics in the non-stationary Ornstein–Uhlenbeck process

Abstract

In this paper, we study Cramér-type moderate deviations for parameter estimation in the non-stationary Ornstein–Uhlenbeck process. The main methods include the deviation inequalities for multiple Wiener-Itô integrals, as well as the asymptotic analysis techniques. For applications, we propose a test statistic which can be used to construct a rejection region in the hypothesis testing for the drift coefficient. It is shown that the probability of type II error tends to zero exponentially when using the proposed test statistic.