Modelling NASDAQ Series by Sparse Multifractional Brownian Motion

被引：0
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作者：
Pierre R. Bertrand
Abdelkader Hamdouni
Samia Khadhraoui
机构：
[1] INRIA Saclay and Clermont Université,Laboratoire de Mathématiques UMR CNRS
[2] University of Monastir,Computational Mathematics Laboratory, Faculté des Sciences
[3] Institut Supérieur de Gestion,undefined
来源：
Methodology and Computing in Applied Probability | 2012年 / 14卷
关键词：
Model selection; Finance; Fractional Brownian motion; Multi-fractional Brownian motion; Generalized quadratic variation; Wavelet analysis; 60G20; 62M09; 62P05; 91B70; 91B84;
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摘要：
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.
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页码：107 / 124
页数：17
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