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Forecasting volatility under fractality, regime-switching, long memory and student-t innovations

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  • Lux, Thomas
  • Morales-Arias, Leonardo

Abstract

The Markov-switching Multifractal model of asset returns with Student-t innovations (MSM-t henceforth) is introduced as an extension to the Markov-switching Multifractal model of asset returns (MSM). The MSM-t can be estimated via Maximum Likelihood (ML) and Generalized Method of Moments (GMM) and volatility forecasting can be performed via Bayesian updating (ML) or best linear forecasts (GMM). Monte Carlo simulations show that using GMM plus linear forecasts leads to minor losses in efficiency compared to optimal Bayesian forecasts based on ML estimates. The forecasting capability of the MSM-t model is evaluated empirically in a comprehensive panel forecasting analysis with three different cross-sections of assets at the country level (all-share equity indices, bond indices and real estate security indices). Empirical forecasts of the MSM-t model are compared to those obtained from its Gaussian counterparts and other volatility models of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family. In terms of mean absolute errors (mean squared errors), the MSM-t (Gaussian MSM) dominates all other models at most forecasting horizons for the various asset classes considered. Furthermore, forecast combinations obtained from the MSM and (Fractionally Integrated) GARCH models provide an improvement upon forecasts from single models.

Suggested Citation

  • Lux, Thomas & Morales-Arias, Leonardo, 2010. "Forecasting volatility under fractality, regime-switching, long memory and student-t innovations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2676-2692, November.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:11:p:2676-2692
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, pages 3730-3742.
    2. Mawuli Segnon & Mark Trede, 2017. "Forecasting Market Risk of Portfolios: Copula-Markov Switching Multifractal Approach," CQE Working Papers 6617, Center for Quantitative Economics (CQE), University of Muenster.
    3. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW).
    4. Adnen Ben Nasr & Ahdi Noomen Ajmi & Rangan Gupta, 2014. "Modelling the volatility of the Dow Jones Islamic Market World Index using a fractionally integrated time-varying GARCH (FITVGARCH) model," Applied Financial Economics, Taylor & Francis Journals, pages 993-1004.
    5. Segnon, Mawuli & Lux, Thomas & Gupta, Rangan, 2015. "Modeling and Forecasting Carbon Dioxide Emission Allowance Spot Price Volatility: Multifractal vs. GARCH-type Volatility Models," FinMaP-Working Papers 46, Collaborative EU Project FinMaP - Financial Distortions and Macroeconomic Performance: Expectations, Constraints and Interaction of Agents.
    6. Segnon, Mawuli & Lux, Thomas & Gupta, Rangan, 2017. "Modeling and forecasting the volatility of carbon dioxide emission allowance prices: A review and comparison of modern volatility models," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 692-704.
    7. Kwan, Wilson & Li, Wai Keung & Li, Guodong, 2012. "On the estimation and diagnostic checking of the ARFIMA–HYGARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3632-3644.
    8. Dias, José G. & Vermunt, Jeroen K. & Ramos, Sofia, 2015. "Clustering financial time series: New insights from an extended hidden Markov model," European Journal of Operational Research, Elsevier, vol. 243(3), pages 852-864.
    9. Joanna Janczura & Rafał Weron, 2013. "Goodness-of-fit testing for the marginal distribution of regime-switching models with an application to electricity spot prices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(3), pages 239-270, July.
    10. Janczura, Joanna & Weron, Rafal, 2010. "Goodness-of-fit testing for regime-switching models," MPRA Paper 22871, University Library of Munich, Germany.
    11. Liu, Yufang & Zhang, Weiguo & Fu, Junhui, 2016. "Binomial Markov-Switching Multifractal model with Skewed t innovations and applications to Chinese SSEC Index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 56-66.
    12. Diniz, Ana & Barreiros, João & Crato, Nuno, 2012. "A new model for explaining long-range correlations in human time interval production," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1908-1919.
    13. Ke Yang & Langnan Chen, 2014. "Realized Volatility Forecast: Structural Breaks, Long Memory, Asymmetry, and Day-of-the-Week Effect," International Review of Finance, International Review of Finance Ltd., vol. 14(3), pages 345-392, September.
    14. Liu, Ruipeng & Lux, Thomas, 2010. "Flexible and robust modelling of volatility comovements: a comparison of two multifractal models," Kiel Working Papers 1594, Kiel Institute for the World Economy (IfW).
    15. Vortelinos, Dimitrios I., 2015. "Out-of-sample evaluation of macro announcements, linearity, long memory, heterogeneity and jumps in mini-futures markets," Review of Financial Economics, Elsevier, vol. 27(C), pages 58-67.

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