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On wavelet analysis of the nth order fractional Brownian motion

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  • Hedi Kortas
  • Zouhaier Dhifaoui
  • Samir Ben Ammou

Abstract

In this paper, we investigate the use of wavelet techniques in the study of the nth order fractional Brownian motion (n-fBm). First, we exploit the continuous wavelet transform’s capabilities in derivative calculation to construct a two-step estimator of the scaling exponent of the n-fBm process. We show, via simulation, that the proposed method improves the estimation performance of the n-fBm signals contaminated by large-scale noise. Second, we analyze the statistical properties of the n-fBm process in the time-scale plan. We demonstrate that, for a convenient choice of the wavelet basis, the discrete wavelet detail coefficients of the n-fBm process are stationary at each resolution level whereas their variance exhibits a power-law behavior. Using the latter property, we discuss a weighted least squares regression based-estimator for this class of stochastic process. Experiments carried out on simulated and real-world datasets prove the relevance of the proposed method. Copyright Springer-Verlag 2012

Suggested Citation

  • Hedi Kortas & Zouhaier Dhifaoui & Samir Ben Ammou, 2012. "On wavelet analysis of the nth order fractional Brownian motion," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 251-277, August.
    • Handle: RePEc:spr:stmapp:v:21:y:2012:i:3:p:251-277
    DOI: 10.1007/s10260-012-0187-2
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    References listed on IDEAS

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