Estimation of the Hurst parameter in some fractional processes

Abstract

We propose to estimate the Hurst parameter involved in fractional processes via a method based on the Karhunen–Loève expansion of a Gaussian process. We specifically investigate the cases of the fractional Brownian motion, the fractional Ornstein–Uhlenbeck family and the fractional Brownian bridge. We numerically compare our results with the ones obtained by the maximum-likelihood method, which show the validity of our proposal.

Keywords:

• Karhunen–Loève expansion
• fractional Gaussian process
• Hurst parameter estimation

AMS Subject Classification :

• 60G22
• 62F10
• 60G15
• 62M05
• 62M15