Volatility estimation of general Gaussian Ornstein–Uhlenbeck process

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.