Volatility estimation of general Gaussian Ornstein–Uhlenbeck process

Qian Yu and Salwa Bajja

Statistics & Probability Letters, 2020, vol. 163, issue C

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.

Keywords: Gaussian process; Quadratic variation; Volatility (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spl.2020.108796

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