Asymptotic properties for the parameter estimation in ornstein-uhlenbeck process with discrete observations

Hui Jiang*, Hui Liu, Youzhou Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

In this paper, under discrete observations, we study Cramértype 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.

Original languageEnglish
Pages (from-to)3192-3229
Number of pages38
JournalElectronic Journal of Statistics
Volume14
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Discrete observations
  • Moderate deviation principle
  • Multiple Wiener-Itô integrals
  • Ornstein-Uhlenbeck process

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