2007/10/01 by Arnaud Gloter, Marc Hoffmann · 47 citations
Economics, Econometrics and Finance · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Brownian motion #Complex Systems and Time Series Analysis #Computer science #Detrended fluctuation analysis #Estimation theory #Estimator #Financial Risk and Volatility Modeling #Fractional Brownian motion #Hurst exponent #Mathematics #Noise (video) #Quadratic equation #Statistics #Stochastic processes and financial applications #math.ST #msc:60G18 #msc:62F12 #msc:62G99 #msc:62M09 #stat.TH
paper · pdf · doi:10.1214/009053607000000316
published in The Annals of Statistics 35(5) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/009053607000000316 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2007/10/01 · arxiv created 2007/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We estimate the Hurst parameter H of a fractional Brownian motion from discrete noisy data observed along a high frequency sampling scheme. The presence of systematic experimental noise makes recovery of H more difficult since relevant information is mostly contained in the high frequencies of the signal. We quantify the difficulty of the statistical problem in a min-max sense: we prove that the rate n−1/(4H+2) is optimal for estimating H and propose rate optimal estimators based on adaptive estimation of quadratic functionals.