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How useful are historical data for forecasting the long-run equity return distribution?

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  • John M Maheu
  • Thomas H McCurdy
Abstract
We provide an approach to forecasting the long-run (unconditional) distribution of equity returns making optimal use of historical data in the presence of structural breaks. Our focus is on learning about breaks in real time and assessing their impact on out-of-sample density forecasts. Forecasts use a probability-weighted average of submodels, each of which is estimated over a different history of data. The paper illustrates the importance of uncertainty about structural breaks and the value of modeling higher-order moments of excess returns when forecasting the return distribution and its moments. The shape of the long-run distribution and the dynamics of the higher-order moments are quite different from those generated by forecasts which cannot capture structural breaks. The empirical results strongly reject ignoring structural change in favor of our forecasts which weight historical data to accommodate uncertainty about structural breaks. We also strongly reject the common practice of using a fixed-length moving window. These differences in long-run forecasts have implications for many financial decisions, particularly for risk management and long-run investment decisions.

Suggested Citation

  • John M Maheu & Thomas H McCurdy, 2007. "How useful are historical data for forecasting the long-run equity return distribution?," Working Papers tecipa-293, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-293
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    Cited by:

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    3. Georges Dionne & Olfa Maalaoui Chun, 2013. "Default and liquidity regimes in the bond market during the 2002-2012 period," Canadian Journal of Economics, Canadian Economics Association, vol. 46(4), pages 1160-1195, November.
    4. Maheu, John M. & Song, Yong, 2014. "A new structural break model, with an application to Canadian inflation forecasting," International Journal of Forecasting, Elsevier, vol. 30(1), pages 144-160.
    5. Andrew Ang & Allan Timmermann, 2012. "Regime Changes and Financial Markets," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 313-337, October.
    6. Ida Wolden Bache & James Mitchell & Francesco Ravazzolo & Shaun P. Vahey, 2009. "Macro modelling with many models," Working Paper 2009/15, Norges Bank.
    7. Yoontae Jeon & Thomas H. McCurdy, 2017. "Time-Varying Window Length for Correlation Forecasts," Econometrics, MDPI, vol. 5(4), pages 1-29, December.
    8. Jiawen Xu & Pierre Perron, 2015. "Forecasting in the presence of in and out of sample breaks," Boston University - Department of Economics - Working Papers Series wp2015-012, Boston University - Department of Economics.
    9. He, Zhongfang & Maheu, John M., 2010. "Real time detection of structural breaks in GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2628-2640, November.
    10. Knut Are Aastveit & James Mitchell & Francesco Ravazzolo & Herman van Dijk, 2018. "The Evolution of Forecast Density Combinations in Economics," Tinbergen Institute Discussion Papers 18-069/III, Tinbergen Institute.
    11. Georges Dionne & Olfa Maalaoui Chun, 2013. "Presidential Address: Default and liquidity regimes in the bond market during the 2002–2012 period," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 46(4), pages 1160-1195, November.
    12. De Angelis Luca & Viroli Cinzia, 2017. "A Markov-switching regression model with non-Gaussian innovations: estimation and testing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(2), pages 1-22, April.
    13. Mwasi Paza Mboya & Philipp Sibbertsen, 2023. "Optimal forecasts in the presence of discrete structural breaks under long memory," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(7), pages 1889-1908, November.
    14. Daniele Bianchi & Massimo Guidolin & Francesco Ravazzolo, 2017. "Macroeconomic Factors Strike Back: A Bayesian Change-Point Model of Time-Varying Risk Exposures and Premia in the U.S. Cross-Section," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 110-129, January.
    15. Yong Song, 2014. "Modelling Regime Switching And Structural Breaks With An Infinite Hidden Markov Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 825-842, August.
    16. Jochmann, Markus & Koop, Gary & Strachan, Rodney W., 2010. "Bayesian forecasting using stochastic search variable selection in a VAR subject to breaks," International Journal of Forecasting, Elsevier, vol. 26(2), pages 326-347, April.
    17. Huang, Yan & Kou, Gang & Peng, Yi, 2017. "Nonlinear manifold learning for early warnings in financial markets," European Journal of Operational Research, Elsevier, vol. 258(2), pages 692-702.
    18. Allan Timmermann, 2018. "Forecasting Methods in Finance," Annual Review of Financial Economics, Annual Reviews, vol. 10(1), pages 449-479, November.
    19. He, Zhongfang, 2009. "Forecasting output growth by the yield curve: the role of structural breaks," MPRA Paper 28208, University Library of Munich, Germany.
    20. Francesco Ravazzolo & Shaun P Vahey, 2010. "Measuring Core Inflation in Australia with Disaggregate Ensembles," RBA Annual Conference Volume (Discontinued), in: Renée Fry & Callum Jones & Christopher Kent (ed.),Inflation in an Era of Relative Price Shocks, Reserve Bank of Australia.
    21. Jiawen Xu & Pierre Perron, 2023. "Forecasting in the presence of in-sample and out-of-sample breaks," Empirical Economics, Springer, vol. 64(6), pages 3001-3035, June.
    22. Meligkotsidou, Loukia & Tzavalis, Elias & Vrontos, Ioannis, 2017. "On Bayesian analysis and unit root testing for autoregressive models in the presence of multiple structural breaks," Econometrics and Statistics, Elsevier, vol. 4(C), pages 70-90.

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    More about this item

    Keywords

    density forecasts; structural change; model risk; parameter uncertainty; Bayesian learning; market returns;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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