Estimation of the global regularity of a multifractional Brownian motion
Estimation de la régularité globale de la régularité d'un mouvement brownien multifractionnaire
Abstract
This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional Brownian motion at two different frequencies. We show that a logarithmic transformation of this statistic converges in probability to the minimum of the Hurst function, which is, under weak assumptions, identical to the global regularity index of the path.
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