Parameter estimation for the discretely observed fractional Ornstein–Uhlenbeck process and the Yuima R package

Abstract

This paper proposes consistent and asymptotically Gaussian estimators for the parameters $$\lambda , \sigma $$ and $$H$$ of the discretely observed fractional Ornstein–Uhlenbeck process solution of the stochastic differential equation $$d Y_t = -\lambda Y_t dt + \sigma d W_t^H$$ , where $$(W_t^H, t\ge 0)$$ is the fractional Brownian motion. For the estimation of the drift $$\lambda $$ , the results are obtained only in the case when $$\frac{1}{2} < H < \frac{3}{4}$$ . This paper also provides ready-to-use software for the R statistical environment based on the YUIMA package.