  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.
