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Modelling NASDAQ Series by Sparse Multifractional Brownian Motion

Author

Listed:
  • Pierre R. Bertrand

    (INRIA Saclay and Clermont Université)

  • Abdelkader Hamdouni

    (University of Monastir)

  • Samia Khadhraoui

    (Institut Supérieur de Gestion)

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.

Suggested Citation

  • Pierre R. Bertrand & Abdelkader Hamdouni & Samia Khadhraoui, 2012. "Modelling NASDAQ Series by Sparse Multifractional Brownian Motion," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 107-124, March.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:1:d:10.1007_s11009-010-9188-5
    DOI: 10.1007/s11009-010-9188-5
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    References listed on IDEAS

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    Cited by:

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    2. Pierre R. Bertrand & Marie-Eliette Dury & Bing Xiao, 2020. "A study of Chinese market efficiency, Shanghai versus Shenzhen: Evidence based on multifractional models," Post-Print hal-03031766, HAL.
    3. Peng, Qidi & Zhao, Ran, 2018. "A general class of multifractional processes and stock price informativeness," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 248-267.

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