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May 2014 Efficient maximum likelihood estimation for Lévy-driven Ornstein–Uhlenbeck processes
Hilmar Mai
Bernoulli 20(2): 919-957 (May 2014). DOI: 10.3150/13-BEJ510

Abstract

We consider the problem of efficient estimation of the drift parameter of an Ornstein–Uhlenbeck type process driven by a Lévy process when high-frequency observations are given. The estimator is constructed from the time-continuous likelihood function that leads to an explicit maximum likelihood estimator and requires knowledge of the continuous martingale part. We use a thresholding technique to approximate the continuous part of the process. Under suitable conditions, we prove asymptotic normality and efficiency in the Hájek–Le Cam sense for the resulting drift estimator. Finally, we investigate the finite sample behavior of the method and compare our approach to least squares estimation.

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Hilmar Mai. "Efficient maximum likelihood estimation for Lévy-driven Ornstein–Uhlenbeck processes." Bernoulli 20 (2) 919 - 957, May 2014. https://doi.org/10.3150/13-BEJ510

Information

Published: May 2014
First available in Project Euclid: 28 February 2014

zbMATH: 06291826
MathSciNet: MR3178522
Digital Object Identifier: 10.3150/13-BEJ510

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

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Vol.20 • No. 2 • May 2014
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