Modelling NASDAQ Series by Sparse Multifractional Brownian Motion

Pierre R. Bertrand (), Abdelkader Hamdouni () and Samia Khadhraoui ()
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Pierre R. Bertrand: INRIA Saclay and Clermont Université
Abdelkader Hamdouni: University of Monastir
Samia Khadhraoui: Institut Supérieur de Gestion

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 1, 107-124

Abstract: Abstract The objective of this paper is to compare the performance of different estimators of Hurst index for multifractional Brownian motion (mBm), namely, Generalized Quadratic Variation (GQV) Estimator, Wavelet Estimator and Linear Regression GQV Estimator. Both estimators are used in the real financial dataset Nasdaq time series from 1971 to the 3rd quarter of 2009. Firstly, we review definitions, properties and statistical studies of fractional Brownian motion (fBm) and mBm. Secondly, a numerical artifact is observed: when we estimate the time varying Hurst index H(t) for an mBm, sampling fluctuation gives the impression that H(t) is itself a stochastic process, even when H(t) is constant. To avoid this artifact, we introduce sparse modelling for mBm and apply it to Nasdaq time series.

Keywords: Model selection; Finance; Fractional Brownian motion; Multi-fractional Brownian motion; Generalized quadratic variation; Wavelet analysis; 60G20; 62M09; 62P05; 91B70; 91B84 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11009-010-9188-5

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