Parameter Estimation for Long-Memory Stochastic Volatility at Discrete Observation

Abstract

Ordinary least squares estimators of variogram parameters in long-memory stochastic volatility are studied in this paper. We use the discrete observations for practical purposes under the assumption that the Hurst parameter $H\in (1/\mathrm{2,1})$ is known. Based on the ordinary least squares method, we obtain both the explicit estimators for drift and diffusion by minimizing the distance function between the variogram and the data periodogram. Furthermore, the resulting estimators are shown to be consistent and to have the asymptotic normality. Numerical examples are also presented to illustrate the performance of our method.