Open AccessVisual information and expert’s idea in Hurst index estimation of the fractional Brownian motion using a diffusion type approximation
Author(s) -
Ali Reza Taheriyoun,
Meisam Moghimbeygi
Publication year - 2017
Publication title -
scientific reports
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.24
H-Index - 213
ISSN - 2045-2322
DOI - 10.1038/srep42482
Subject(s) - fractional brownian motion , estimator , hurst exponent , mathematics , realization (probability) , brownian motion , computer science , likelihood function , bayesian probability , estimation theory , statistics
An approximation of the fractional Brownian motion based on the Ornstein-Uhlenbeck process is used to obtain an asymptotic likelihood function. Two estimators of the Hurst index are then presented in the likelihood approach. The first estimator is produced according to the observed values of the sample path; while the second one employs the likelihood function of the incremental process. We also employ visual roughness of realization to restrict the parameter space and to obtain prior information in Bayesian approach. The methods are then compared with three contemporary estimators and an experimental data set is studied.