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.

KEYWORDS:

• Deviation inequalities
• maximum likelihood estimator
• moderate deviation principle
• multiple Wiener-Itô integrals
• non-stationary Ornstein–Uhlenbeck process

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62N02
• 60F10
• 60G22

Acknowledgements

The authors would like to express great gratitude to the two anonymous referees and the editor for the careful reading and constructive comments which led to an improved presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Hui Jiang is supported by the National Natural Science Foundation of China (Grant No. 11771209).