Statistical inference for Vasicek-type model driven by Hermite processes

Ivan Nourdin and T.T. Diu Tran

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 3774-3791

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.

Keywords: Parameter estimation; Strong consistency; Fractional Ornstein–Uhlenbeck process; Hermite Ornstein–Uhlenbeck processes; Fractional Vasicek model; Long-range dependence (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:10:p:3774-3791

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DOI: 10.1016/j.spa.2018.10.005

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