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2020 Asymptotic properties for the parameter estimation in Ornstein-Uhlenbeck process with discrete observations
Hui Jiang, Hui Liu, Youzhou Zhou
Electron. J. Statist. 14(2): 3192-3229 (2020). DOI: 10.1214/20-EJS1738

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.

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Hui Jiang. Hui Liu. Youzhou Zhou. "Asymptotic properties for the parameter estimation in Ornstein-Uhlenbeck process with discrete observations." Electron. J. Statist. 14 (2) 3192 - 3229, 2020. https://doi.org/10.1214/20-EJS1738

Information

Received: 1 January 2020; Published: 2020
First available in Project Euclid: 5 September 2020

zbMATH: 07246816
MathSciNet: MR4146360
Digital Object Identifier: 10.1214/20-EJS1738

Subjects:
Primary: 60F10, 60G22, 62N02

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Vol.14 • No. 2 • 2020
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