Hurst index estimation for self-similar processes with long-memory

Alexandra Chronopoulou, Frederi G. Viens

Research output: Chapter in Book/Report/Conference proceedingChapter


The statistical estimation of the Hurst index is one of the fundamental problems in the literature of long-range dependent and self-similar processes. In this article, the Hurst index estimation problem is addressed for a special class of self-similar processes that exhibit long-memory, the Hermite processes. These processes generalize the fractional Brownian motion, in the sense that they share its covariance function, but are non-Gaussian. Existing estimators such as the R/S statistic, the variogram, the maximum likelihood and the wavelet-based estimators are reviewed and compared with a class of consistent estimators which are constructed based on the discrete variations of the process. Convergence theorems (asymptotic distributions) of the latter are derived using multiple Wiener-Itô integrals and Malliavin calculus techniques. Based on these results, it is shown that the latter are asymptotically more efficient than the former.

Original languageEnglish (US)
Title of host publicationRecent Development In Stochastic Dynamics And Stochastic Analysis
PublisherWorld Scientific Publishing Co. Pte Ltd
Number of pages27
ISBN (Electronic)9789814277266
ISBN (Print)9789814277259
StatePublished - Feb 8 2010
Externally publishedYes


  • Fractional Brownian motion
  • Hermite process
  • Hurst parameter
  • Long memory
  • Malliavin calculus
  • Multiple stochastic integral
  • Non-central limit theorem
  • Parameter estimation
  • Quadratic variation
  • Self-similar process

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Hurst index estimation for self-similar processes with long-memory'. Together they form a unique fingerprint.

Cite this