Department of Economics and Business Economics

Estimation of the global regularity of a multifractional Brownian motion

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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 functional parameter, which is, under weak assumptions, identical to the global regularity index of the path.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages17
Publication statusPublished - 9 Dec 2016
SeriesCREATES Research Papers
Number2016-33

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