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

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

Hilmar Mai

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

First available in Project Euclid: 28 February 2014

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discrete time observations efficient drift estimation jump filtering Lévy process maximum likelihood estimation Ornstein–Uhlenbeck process


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

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