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Modeling and Forecasting S&P 500 Volatility: Long Memory, Structural Breaks and Nonlinearity

Author

Listed:
  • Martin Martens

    (Faculty of Economics, Erasmus Universiteit Rotterdam)

  • Dick van Dijk

    (Faculty of Economics, Erasmus Universiteit Rotterdam)

  • Michiel de Pooter

    (Faculty of Economics, Erasmus Universiteit Rotterdam)

Abstract

This discussion paper resulted in a publication in the 'International Journal of Forecasting', 2009, 27, 282-303. The sum of squared intraday returns provides an unbiased and almost error-free measure of ex-post volatility. In this paper we develop a nonlinear Autoregressive Fractionally Integrated Moving Average (ARFIMA) model for realized volatility, which accommodates level shifts, day-of-the-week effects, leverage effects and volatility level effects. Applying the model to realized volatilities of the S&P 500 stock index and three exchange rates produces forecasts that clearly improve upon the ones obtained from a linear ARFIMA model and from conventional time-series models based on daily returns, treating volatility as a latent variable.

Suggested Citation

  • Martin Martens & Dick van Dijk & Michiel de Pooter, 2004. "Modeling and Forecasting S&P 500 Volatility: Long Memory, Structural Breaks and Nonlinearity," Tinbergen Institute Discussion Papers 04-067/4, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20040067
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Nasr, Adnen Ben & Lux, Thomas & Ajmi, Ahdi Noomen & Gupta, Rangan, 2016. "Forecasting the volatility of the Dow Jones Islamic Stock Market Index: Long memory vs. regime switching," International Review of Economics & Finance, Elsevier, vol. 45(C), pages 559-571.
    2. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
    3. repec:zbw:cfswop:wp200533 is not listed on IDEAS
    4. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    5. Bollerslev, Tim & Kretschmer, Uta & Pigorsch, Christian & Tauchen, George, 2009. "A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects," Journal of Econometrics, Elsevier, vol. 150(2), pages 151-166, June.
    6. Chun Liu & John M. Maheu, 2008. "Are There Structural Breaks in Realized Volatility?," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(3), pages 326-360, Summer.
    7. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    9. Maheu, John M. & McCurdy, Thomas H., 2011. "Do high-frequency measures of volatility improve forecasts of return distributions?," Journal of Econometrics, Elsevier, vol. 160(1), pages 69-76, January.
    10. Offer Lieberman & Peter Phillips, 2008. "Refined Inference on Long Memory in Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 254-267.
    11. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    12. Shi, Yanlin & Ho, Kin-Yip, 2015. "Modeling high-frequency volatility with three-state FIGARCH models," Economic Modelling, Elsevier, vol. 51(C), pages 473-483.
    13. Di Sanzo, Silvestro, 2018. "A Markov switching long memory model of crude oil price return volatility," Energy Economics, Elsevier, vol. 74(C), pages 351-359.
    14. Matei, Marius, 2011. "Non-Linear Volatility Modeling of Economic and Financial Time Series Using High Frequency Data," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 116-141, June.
    15. Morana, Claudio, 2009. "On the macroeconomic causes of exchange rate volatility," International Journal of Forecasting, Elsevier, vol. 25(2), pages 328-350.
    16. Chun Liu & John M. Maheu, 2009. "Forecasting realized volatility: a Bayesian model-averaging approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 709-733.
    17. Trunin, Pavel (Трунин, Павел), 2015. "Analysis of the Level of Development of the Financial System in the Russian Federation [Анализ Уровня Развития Финансовой Системы В Российской Федерации]," Published Papers mn38, Russian Presidential Academy of National Economy and Public Administration.
    18. Adnen Ben Nasr & Mohamed Boutahar & Abdelwahed Trabelsi, 2010. "Fractionally integrated time varying GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 399-430, August.
    19. Maurício Yoshinori Une & Marcelo Savino Portugal, 2005. "Can fear beat hope? A story of GARCH-in-Mean-Level effects for Emerging Market Country Risks," Econometrics 0509006, University Library of Munich, Germany.
    20. Kasman, Adnan & Kasman, Saadet & Torun, Erdost, 2009. "Dual long memory property in returns and volatility: Evidence from the CEE countries' stock markets," Emerging Markets Review, Elsevier, vol. 10(2), pages 122-139, June.
    21. Claudio Morana, 2007. "Estimating, Filtering and Forecasting Realized Betas," ICER Working Papers - Applied Mathematics Series 6-2007, ICER - International Centre for Economic Research.

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    More about this item

    Keywords

    Realized volatility; high-frequency data; long memory; day-of-the-week effect; leverage effect; volatility forecasting; smooth transition;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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