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Volatility estimation of general Gaussian Ornstein–Uhlenbeck process

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  • Yu, Qian
  • Bajja, Salwa

Abstract

In this article we study the asymptotic behavior of the realized quadratic variation of a process ∫0tusdGsH, where u is a Hölder continuous process with order β>1−H and GH is a self-similar Gaussian process with parameter H∈(0,3∕4). We prove almost sure convergence uniformly in time and a stable weak convergence for the realized quadratic variation. As an application, we construct strongly consistent estimator for the integrated volatility parameter in Ornstein–Uhlenbeck process driven by GH.

Suggested Citation

  • Yu, Qian & Bajja, Salwa, 2020. "Volatility estimation of general Gaussian Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 163(C).
    • Handle: RePEc:eee:stapro:v:163:y:2020:i:c:s0167715220300997
    DOI: 10.1016/j.spl.2020.108796
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    References listed on IDEAS

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