Markov-Switching Multifractal
The Markov-Switching Multifractal (MSM) model is a flexible framework for capturing time-varying volatility and long-memory effects in financial time series. Developed by Calvet and Fisher (2004), it combines Markov chain theory with multifractal scaling principles to generate volatility that exhibits multiple frequency components, each switching between high and low regimes. This approach is particularly effective for modeling asset returns with realistic fat tails and clustered volatility.
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- Calvet, L. E., & Fisher, A. J. (2004). How to forecast long-run volatility: regime-switching and the estimation of multifractal processes. Journal of Financial Econometrics, 2(1), 49–83. · DOI 10.1093/jjfinec/nbh003
- Calvet, L. E., & Fisher, A. J. (2008). Multifractal Volatility: Theory, Forecasting, and Pricing. Academic Press. · URL
- Lux, T. (2008). The Markov-switching multifractal model of asset returns: GMM estimation and linear forecasting of volatility. Journal of Business & Economic Statistics, 26(2), 194–210. · DOI 10.1198/073500107000000403
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