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Regime-Switching and the Estimation of Multifractal Processes

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Laurent Calvet
Adlai Fisher

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Abstract

We propose a discrete-time stochastic volatility model in which regime switching serves three purposes. First, changes in regimes capture low frequency variations, which is their traditional role. Second, they specify intermediate frequency dynamics that are usually assigned to smooth autoregressive processes. Finally, high frequency switches generate substantial outliers. Thus, a single mechanism captures three important features of the data that are typically addressed as distinct phenomena in the literature. Maximum likelihood estimation is developed and shown to perform well in finite sample. We estimate on exchange rate data a version of the process with four parameters and more than a thousand states. The estimated model compares favorably to earlier specifications both in- and out-of-sample. Multifractal forecasts slightly improve on GARCH(1,1) at daily and weekly intervals, and provide considerable gains in accuracy at horizons of 10 to 50 days.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9839.

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Date of creation: Jul 2003
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Handle: RePEc:nbr:nberwo:9839

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G0 - Financial Economics - - General
C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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  1. Lux, Thomas, 2004. "The Markov-switching multi-fractal model of asset returns : GMM estimation and linear forecasting of volatility," Economics Working Papers 2004,11, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
    Other versions:
  2. Lux, Thomas, 2003. "The multi-fractal model of asset returns : its estimation via GMM and its use for volatility forecasting," Economics Working Papers 2003,13, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
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  3. Laurent E. Calvet & Adlai J. Fisher, 2005. "Multifrequency News and Stock Returns," NBER Working Papers 11441, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  4. Lux, Thomas & Kaizoji, Taisei, 2004. "Forecasting volatility and volume in the Tokyo stock market : the advantage of long memory models," Economics Working Papers 2004,05, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
  5. Lux, Thomas & Kaizoji, Taisei, 2006. "Forecasting volatility and volume in the Tokyo stock market : long memory, fractality and regime switching," Economics Working Papers 2006,13, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
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