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Statistical inference for Vasicek-type model driven by Hermite processes

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  • Nourdin, Ivan
  • Diu Tran, T.T.

Abstract

Let Z denote a Hermite process of order q≥1 and self-similarity parameter H∈(12,1). This process is H-self-similar, has stationary increments and exhibits long-range dependence. When q=1, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as q⩾2. In this paper, we deal with a Vasicek-type model driven by Z, of the form dXt=a(b−Xt)dt+dZt. Here, a>0 and b∈R are considered as unknown drift parameters. We provide estimators for a and b based on continuous-time observations. For all possible values of H and q, we prove strong consistency and we analyze the asymptotic fluctuations.

Suggested Citation

  • Nourdin, Ivan & Diu Tran, T.T., 2019. "Statistical inference for Vasicek-type model driven by Hermite processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3774-3791.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:3774-3791
    DOI: 10.1016/j.spa.2018.10.005
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    References listed on IDEAS

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    Cited by:

    1. Kerchev, George & Nourdin, Ivan & Saksman, Eero & Viitasaari, Lauri, 2021. "Local times and sample path properties of the Rosenblatt process," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 498-522.
    2. Katsuto Tanaka & Weilin Xiao & Jun Yu, 2020. "Maximum Likelihood Estimation for the Fractional Vasicek Model," Econometrics, MDPI, vol. 8(3), pages 1-28, August.
    3. Daw, Lara & Kerchev, George, 2023. "Fractal dimensions of the Rosenblatt process," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 544-571.
    4. Rachid Belfadli & Khalifa Es-Sebaiy & Fatima-Ezzahra Farah, 2022. "Statistical analysis of the non-ergodic fractional Ornstein–Uhlenbeck process with periodic mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(7), pages 885-911, October.
    5. Khalifa Es-Sebaiy & Mohammed Es.Sebaiy, 2021. "Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 409-436, June.

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