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Fractals

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.
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Submitted on : Sunday, February 19, 2012 - 4:02:11 PM
Last modification on : Thursday, January 11, 2018 - 6:19:31 AM

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Laurent Calvet. Fractals. Steven N. Durlauf and Lawrence E. Blume Eds. The New Palgrave Dictionary of Economics (2nd edition), Palgrave, pp.NC, 2008, ⟨10.1057/9780230226203.0598⟩. ⟨hal-00671878⟩

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