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Long‐range Dependence: Revisiting Aggregation with Wavelets

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  • Patrice Abry
  • Darryl Veitch
  • Patrick Flandrin

Abstract

The aggregation procedure is a natural way to analyse signals which exhibit long‐range‐dependent features and has been used as a basis for estimation of the Hurst parameter, H. In this paper it is shown how aggregation can be naturally rephrased within the wavelet transform framework, being directly related to approximations of the signal in the sense of a Haar multiresolution analysis. A natural wavelet‐based generalization to traditional aggregation is then proposed: ‘a‐aggregation’. It is shown that a‐aggregation cannot lead to good estimators of H, and so a new kind of aggregation, ‘d‐aggregation’, is defined, which is related to the details rather than the approximations of a multiresolution analysis. An estimator of H based on d‐aggregation has excellent statistical and computational properties, whilst preserving the spirit of aggregation. The estimator is applied to telecommunications network data.

Suggested Citation

  • Patrice Abry & Darryl Veitch & Patrick Flandrin, 1998. "Long‐range Dependence: Revisiting Aggregation with Wavelets," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(3), pages 253-266, May.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:3:p:253-266
    DOI: 10.1111/1467-9892.00090
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    Cited by:

    1. Frezza, Massimiliano, 2012. "Modeling the time-changing dependence in stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1510-1520.
    2. Erdinc Akyildirim & Shaen Corbet & Guzhan Gulay & Duc Khuong Nguyen & Ahmet Sensoy, 2019. "Order Flow Persistence in Equity Spot and Futures Markets: Evidence from a Dynamic Emerging Market," Working Papers 2019-011, Department of Research, Ipag Business School.
    3. Rehman, S. & Siddiqi, A.H., 2009. "Wavelet based hurst exponent and fractal dimensional analysis of Saudi climatic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1081-1090.
    4. Rehman, S. & Siddiqi, A.H., 2009. "Wavelet based correlation coefficient of time series of Saudi Meteorological Data," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1764-1789.
    5. Francis In & Sangbae Kim, 2012. "An Introduction to Wavelet Theory in Finance:A Wavelet Multiscale Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8431.

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