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Media type:
E-Article
Title:
Efficient maximum likelihood estimation for Lévy-driven Ornstein-Uhlenbeck processes
Contributor:
MAI, HILMAR
Published:
International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability, 2014
Published in:
Bernoulli, 20 (2014) 2, Seite 919-957
Language:
English
DOI:
10.3150/13-BEJ510
ISSN:
1350-7265
Origination:
Footnote:
Description:
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 Hajek-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.