## Bernoulli

• Bernoulli
• Volume 20, Number 2 (2014), 919-957.

### Efficient maximum likelihood estimation for Lévy-driven Ornstein–Uhlenbeck processes

Hilmar Mai

#### 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.

#### Article information

Source
Bernoulli, Volume 20, Number 2 (2014), 919-957.

Dates
First available in Project Euclid: 28 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1393594010

Digital Object Identifier
doi:10.3150/13-BEJ510

Mathematical Reviews number (MathSciNet)
MR3178522

Zentralblatt MATH identifier
06291826

#### Citation

Mai, Hilmar. Efficient maximum likelihood estimation for Lévy-driven Ornstein–Uhlenbeck processes. Bernoulli 20 (2014), no. 2, 919--957. doi:10.3150/13-BEJ510. https://projecteuclid.org/euclid.bj/1393594010

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