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Description, modeling and forecasting of data with optimal wavelets

Author

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  • Oriol Pont

    (UB - Universitat de Barcelona)

  • Antonio Turiel

    (ICM - Institute of Marine Sciences / Institut de Ciències del Mar [Barcelona] - CSIC - Consejo Superior de Investigaciones Cientificas [España] = Spanish National Research Council [Spain])

  • Conrad J. Perez-Vicente

    (UB - Universitat de Barcelona)

Abstract

Cascade processes have been used to model many different self-similar systems, as they are able to accurately describe most of their global statistical properties. The so-called optimal wavelet basis allows to achieve a geometrical representation of the cascade process-named microcanonical cascade- that describes the behavior of local quantities and thus it helps to reveal the underlying dynamics of the system. In this context, we study the benefits of using the optimal wavelet in contrast to other wavelets when used to define cascade variables, and we provide an optimality degree estimator that is appropriate to determine the closest-to-optimal wavelet in real data. Particularizing the analysis to stock market series, we show that they can be represented by microcanonical cascades in both the logarithm of the price and the volatility. Also, as a promising application in forecasting, we derive the distribution of the value of next point of the series conditioned to the knowledge of past points and the cascade structure, i.e., the stochastic kernel of the cascade process.

Suggested Citation

  • Oriol Pont & Antonio Turiel & Conrad J. Perez-Vicente, 2009. "Description, modeling and forecasting of data with optimal wavelets," Post-Print inria-00438526, HAL.
    • Handle: RePEc:hal:journl:inria-00438526
    DOI: 10.1007/s11403-009-0046-x
    Note: View the original document on HAL open archive server: https://inria.hal.science/inria-00438526
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    References listed on IDEAS

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    1. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
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    3. J-F. Muzy & D. Sornette & J. delour & A. Arneodo, 2001. "Multifractal returns and hierarchical portfolio theory," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 131-148.
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