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Generalized moment estimators for \(\alpha \)-stable Ornstein–Uhlenbeck motions from discrete observations

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Abstract

We study the parameter estimation problem for discretely observed Ornstein–Uhlenbeck processes driven by \(\alpha \)-stable Lévy motions. A method of moments via ergodic theory and via sample characteristic functions is proposed to estimate all the parameters involved in the Ornstein–Uhlenbeck processes. We obtain the strong consistency and asymptotic normality of the proposed joint estimators when the sample size \(n \rightarrow \infty \) while the sampling time step h remains arbitrarily fixed. We also design a procedure to select the grid points in the characteristic functions in certain optimal way for the proposed estimators.

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Acknowledgements

The authors are grateful to the anonymous referees, the associate editor and the editor for their insightful and valuable comments which have greatly improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, The University of Kansas, Lawrence, KS, 66045, USA

    Yiying Cheng

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Yaozhong Hu

  3. Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, 33431-0991, USA

    Hongwei Long

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  1. Yiying Cheng
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  2. Yaozhong Hu
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  3. Hongwei Long
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Correspondence to Hongwei Long.

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Yaozhong Hu was partially supported by an NSERC discovery grant and a start-up fund from University of Alberta.

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Cheng, Y., Hu, Y. & Long, H. Generalized moment estimators for \(\alpha \)-stable Ornstein–Uhlenbeck motions from discrete observations. Stat Inference Stoch Process 23, 53–81 (2020). https://doi.org/10.1007/s11203-019-09201-4

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  • DOI: https://doi.org/10.1007/s11203-019-09201-4

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