Variance estimation for fractional brownian motions with fixed hurst parameters

Jean François Coeurjolly, Kichun Lee, Brani Vidakovic

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

Some real-world phenomena in geo-science, micro-economy, and turbulence, to name a few, can be effectively modeled by a fractional Brownian motion indexed by a Hurst parameter, a regularity level, and a scaling parameter σ2, an energy level. This article discusses estimation of a scaling parameter σ2 when a Hurst parameter is known. To estimate σ2, we propose three approaches based on maximum likelihood estimation, moment-matching, and concentration inequalities, respectively, and discuss the theoretical characteristics of the estimators and optimal-filtering guidelines. We also justify the improvement of the estimation of σ2 when a Hurst parameter is known. Using the three approaches and a parametric bootstrap methodology in a simulation study, we compare the confidence intervals of σ2 in terms of their lengths, coverage rates, and computational complexity and discuss empirical attributes of the tested approaches. We found that the approach based on maximum likelihood estimation was optimal in terms of efficiency and accuracy, but computationally expensive. The moment-matching approach was found to be not only comparably efficient and accurate but also computationally fast and robust to deviations from the fractional Brownian motion model.

Original languageEnglish
Pages (from-to)1845-1858
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Volume43
Issue number8
DOIs
StatePublished - 2014 Apr 18

Keywords

  • Fractional Brownian motion
  • Hurst exponent
  • Turbulence signals
  • Variance estimation

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