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Estimation of the global regularity of a multifractional Brownian motion

Joachim Lebovits () and Mark Podolskij ()
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Joachim Lebovits: University Paris 13, Postal: Laboratoire Analyse, Géométrie et Applications, C.N.R.S. (UMR 7539), Université Paris 13, Sorbonne Paris Cité, 99 avenue Jean-Baptiste Clément 93430, Villetaneuse, France
Mark Podolskij: Aarhus University and CREATES, Postal: Department of Mathematics, University of Aarhus, Ny Munkegade 118, 8000 Aarhus C, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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 functional parameter, which is, under weak assumptions, identical to the global regularity index of the path.

Keywords: consistency; Hurst parameter; multifractional Brownian motion; power variation (search for similar items in EconPapers)
JEL-codes: C10 C13 C14 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2016-12-06
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