Quasi-likelihood analysis of fractional Brownian motion with constant drift under high-frequency observations

Abstract

Consider an estimation of the Hurst parameter H∈(0,1) and the volatility parameter σ>0 for a fractional Brownian motion with a drift term under high-frequency observations with a finite time interval. In the present paper, we propose a consistent estimator of the parameter θ=(H,σ) combining the ideas of a quasi-likelihood function based on a local Gaussian approximation of a high-frequently observed time series and its frequency-domain approximation. Moreover, we prove an asymptotic normality property of the proposed estimator for all H∈(0,1) when the drift process is constant.