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Drift estimation for a Lévy-driven Ornstein–Uhlenbeck process with heavy tails

Author

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  • Alexander Gushchin

    (Steklov Mathematical Institute of Russian Academy of Sciences
    National Research University Higher School of Economics)

  • Ilya Pavlyukevich

    (Friedrich Schiller University Jena)

  • Marian Ritsch

    (Friedrich Schiller University Jena)

Abstract

We consider the problem of estimation of the drift parameter of an ergodic Ornstein–Uhlenbeck type process driven by a Lévy process with heavy tails. The process is observed continuously on a long time interval [0, T], $$T\rightarrow \infty $$ T → ∞ . We prove that the statistical model is locally asymptotic mixed normal and the maximum likelihood estimator is asymptotically efficient.

Suggested Citation

  • Alexander Gushchin & Ilya Pavlyukevich & Marian Ritsch, 2020. "Drift estimation for a Lévy-driven Ornstein–Uhlenbeck process with heavy tails," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 553-570, October.
    • Handle: RePEc:spr:sistpr:v:23:y:2020:i:3:d:10.1007_s11203-020-09210-8
    DOI: 10.1007/s11203-020-09210-8
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    References listed on IDEAS

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    1. Ngoc Khue Tran, 2017. "LAN property for an ergodic Ornstein–Uhlenbeck process with Poisson jumps," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 7942-7968, August.
    2. Masuda, Hiroki, 2019. "Non-Gaussian quasi-likelihood estimation of SDE driven by locally stable Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 1013-1059.
    3. Long, Hongwei, 2009. "Least squares estimator for discretely observed Ornstein-Uhlenbeck processes with small Lévy noises," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2076-2085, October.
    4. Shibin Zhang & Xinsheng Zhang, 2013. "A least squares estimator for discretely observed Ornstein–Uhlenbeck processes driven by symmetric α-stable motions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 89-103, February.
    5. Uehara, Yuma, 2019. "Statistical inference for misspecified ergodic Lévy driven stochastic differential equation models," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4051-4081.
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    Cited by:

    1. Valentin Courgeau & Almut E. D. Veraart, 2022. "Likelihood theory for the graph Ornstein-Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 227-260, July.

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