Statistical inference in discretely observed fractional Ornstein–Uhlenbeck processes

Abstract

In this paper, we develop a two-stage method for estimating all the unknown parameters in the fractional Ornstein–Uhlenbeck model from discrete observations. The estimation procedure is built upon the marriage of the power variation and the minimum contrast estimation. In the first stage, the Hurst coefficient is estimated by the increment Bernoulli statistic and the volatility parameter is estimated by power variations. The asymptotic theory of the proposed estimators in the diffusion term are established under an in-fill asymptotic scheme. In the second stage, two drift parameters are estimated based on the minimum contrast estimation. Their asymptotic theory are analyzed via use of a double asymptotic scheme. The results from Monte Carlo studies illustrate that the proposed estimators have reasonable finite sample properties. An empirical illustration based on realized volatility indicates that the realized volatility is rough.