Modelling NASDAQ Series by Sparse Multifractional Brownian Motion |
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| Authors: | Pierre R Bertrand Abdelkader Hamdouni Samia Khadhraoui |
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| Institution: | (1) College of Civil Engineering, Hefei University of Technology, Hefei, 230009, China;(2) Institute of Policy and Management (IPM), Chinese Academy of Sciences (CAS), Beijing, 100080, China; |
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| 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. |
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