Efficient maximum likelihood estimation for Lévy-driven Ornstein–Uhlenbeck processes
| Autor: | Hilmar Mai |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
jump filtering Lévy process Maximum likelihood Asymptotic distribution Estimator Mathematics - Statistics Theory Ornstein–Uhlenbeck process maximum likelihood estimation Thresholding discrete time observations efficient drift estimation Applied mathematics Martingale (probability theory) Likelihood function Mathematics |
| Zdroj: | Bernoulli 20, no. 2 (2014), 919-957 |
| Popis: | We consider the problem of efficient estimation of the drift parameter of an Ornstein-Uhlenbeck type process driven by a L\'{e}vy 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 H\'{a}jek-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. Comment: Published in at http://dx.doi.org/10.3150/13-BEJ510 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) |
| Databáze: | OpenAIRE |
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