The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Fractals

  • Laurent E. Calvet
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2730

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.

Keywords

Bayesian filtering Brownian motion Continuous time valuation Fractals Fractional Brownian motion Lévy-stable processes Long memory models Mandelbrot, B Markov-switching multifractal (MSM) Maximum likelihood Multifractal model of asset returns (MMAR) Multifractality Regime switching Self-similarity processes 
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Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Laurent E. Calvet
    • 1
  1. 1.