Overfitting of Hurst estimators for multifractional Brownian motion: A fitting test advocating simple models

Issue title: Fractional Calculus and Its Applications

Guest editors: Sergio Bianchi

Article type: Research Article

Authors: Bertrand, Pierre Raphaël^{a; b; *} | Combes, Jean-Louis^c | Dury, Marie-Eliette^c | Hadouni, Doha^{a; d}

Affiliations: [a] Université Clermont Auvergne, CNRS, LMBP, F-63000, Clermont-Ferrand, France | [b] Université Clermont Auvergne, CNRS, LaPSCo, F-63000, Clermont-Ferrand, France | [c] Université Clermont Auvergne, CNRS, CERDI, F-63000, Clermont-Ferrand, France | [d] Université Bretagne Sud, CNRS, LMBA, F-56000, Vannes, France

Correspondence: [*] Corresponding author. E-mail: Pierre.Bertrand@uca.fr.

Abstract: The aim of this paper is to provide simple models with a time-varying Hurst index. Such models should be simple as much as possible and well fit the estimated Hurst index. After a recall on the fractional and multifractional Brownian motion and on the statistical estimation of the Hurst index, we propose a fitting test for a model with a time-varying Hurst index. Then, we give an approach to select a simple model. Our approach is illustrated by numerous numerical simulations and then applied to market finance data.

Keywords: Fractional Brownian motion (fBm), multifractional Brownian motion (mBm), time-varying Hurst index, wavelet series expansion, finance time series

DOI: 10.3233/RDA-180136

Journal: Risk and Decision Analysis, vol. 7, no. 1-2, pp. 31-49, 2018