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

TL;DR

This paper develops consistent estimators for key parameters of the fractional Ornstein-Uhlenbeck process observed discretely, focusing on the drift, diffusion, and Hurst exponent, and provides an R package for implementation.

Contribution

It introduces new estimators for the fractional Ornstein-Uhlenbeck process parameters and offers an R package for practical application.

Findings

Estimators are consistent and asymptotically Gaussian.

Effective for Hurst exponent 1/2 < H < 3/4.

Provides software implementation in R.

Abstract

This paper proposes consistent and asymptotically Gaussian estimators for the drift, the diffusion coefficient and the Hurst exponent of the discretely observed fractional Ornstein-Uhlenbeck process. For the estimation of the drift, the results are obtained only in the case when 1/2 < H < 3/4. This paper also provides ready-to-use software for the R statistical environment based on the YUIMA package.