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Fractals

Author

Listed:
  • Laurent E. Calvet

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

Fractals have become increasingly useful tools for the statistical modelling of financial prices. While early research assumed invariance of the return density with the time horizon, new processes have recently been developed to capture nonlinear changes in return dynamics across frequencies. The Markov-switching multifractal (MSM) is a parsimonious stochastic volatility model containing arbitrarily many shocks of heterogeneous durations. MSM captures the outliers, volatility persistence and power variation of financial series, while permitting maximum likelihood estimation and analytical multi-step forecasting. MSM compares favourably with standard volatility models such as GARCH(1,1) both in- and out-of-sample.

Suggested Citation

  • Laurent E. Calvet, 2008. "Fractals," Post-Print hal-00671878, HAL.
    • Handle: RePEc:hal:journl:hal-00671878
    DOI: 10.1057/9780230226203.0598
    as

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