Generalized moment estimators for $$\alpha $$α-stable Ornstein–Uhlenbeck motions from discrete observations

Yiying Cheng (), Yaozhong Hu () and Hongwei Long ()
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Yiying Cheng: The University of Kansas
Yaozhong Hu: University of Alberta
Hongwei Long: Florida Atlantic University

Statistical Inference for Stochastic Processes, 2020, vol. 23, issue 1, No 2, 53-81

Abstract: Abstract We study the parameter estimation problem for discretely observed Ornstein–Uhlenbeck processes driven by $$\alpha $$α-stable Lévy motions. A method of moments via ergodic theory and via sample characteristic functions is proposed to estimate all the parameters involved in the Ornstein–Uhlenbeck processes. We obtain the strong consistency and asymptotic normality of the proposed joint estimators when the sample size $$n \rightarrow \infty $$n→∞ while the sampling time step h remains arbitrarily fixed. We also design a procedure to select the grid points in the characteristic functions in certain optimal way for the proposed estimators.

Keywords: $$\alpha $$ α -Stable Ornstein–Uhlenbeck motions; Discrete time observation; Characteristic functions; Generalized moment estimators; Consistency; Asymptotic normality; 62F12; 62M05; 60G52 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11203-019-09201-4

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