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

  • Authors:

  • Alexandre Brouste;Stefano M. Iacus

  • Affiliations:

  • Laboratoire Manceau de Mathématiques, Université du Maine, Le Mans, France 72100;Department of Economics, Management and Quantitative Methods, University of Milan, Milan, Italy 20122

  • Venue:
  • Computational Statistics
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

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} . This paper also provides ready-to-use software for the R statistical environment based on the YUIMA package.