Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Forecasting volatility using combination across estimation windows: An application to S&P500 stock market index

1 Department of Economics, University of Roma Tre, Via Silvio D’Amico 77, Rome, 00145, Italy
2 SOSE - Soluzioni per il Sistema Economico Spa, Via Mentore Maggini 48C, Rome, 00143, Italy

Special Issues: Advances in Stochastic processes and Applications

The paper focuses on GARCH-type models for analysing and forecasting S&P500 stock market index. The aim is to empirically evaluate and compare alternative forecast combinations across estimation windows for directly dealing with possible structural breaks in the observed time series. In the in-sample analysis, alternative conditional volatility dynamics, suitable to account for stylized facts, have been considered along with different conditional distributions for the innovations. Moreover, an analysis of structural breaks in the unconditional variance of the series has been performed. In the out-of-sample analysis, for each model specification, the proposed forecast combinations have been evaluated and compared in terms of their predictive ability through the model confidence set. The results give evidence of the presence of structural breaks and, as a consequence, of parameter instability in S&P500 series. Moreover, averaging across volatility forecasts generated by individual forecasting models estimated using different window sizes performs well, for all the considered GARCH-type specifications and for all the implemented conditional distributions for the innovations and it appears to offer a useful approach to forecasting S&P500 stock market index.
  Article Metrics

Keywords forecast combinations; structural breaks; volatility forecasting; parameter instability; financial time series

Citation: Davide De Gaetano. Forecasting volatility using combination across estimation windows: An application to S&P500 stock market index. Mathematical Biosciences and Engineering, 2019, 16(6): 7195-7216. doi: 10.3934/mbe.2019361


  • 1. B. Rossi and A. Inoue, Out-of-sample forecast tests robust to the choice of window size, J. Bus. Econ. Stat., 30 (2012), 432–453.
  • 2. D. E. Rapach and J. K. Strauss, Structural breaks and GARCH models of exchange rate volatility, J. Appl. Econom., 23 (2008), 65–90.
  • 3. D. E. Rapach, J. K. Strauss and M. E. Wohar, Chapter 10 Forecasting Stock Return Volatility in the Presence of Structural Breaks, in Forecasting in the presence of structural breaks and model uncertainty, Emerald Group Publishing Limited, (2008), 381–416.
  • 4. A. Timmermann, Chapter 4 Forecast combinations, in Handbook of economic forecasting, (2006), 135–196.
  • 5. M. H. Pesaran and A. Timmermann, Selection of estimation windows in the presence of breaks, J. Econometrics, 137 (2007), 134–161.
  • 6. J. Tian and H. M. Anderson, Forecast combinations under structural break uncertainty, Int. J. Forecasting, 30 (2014), 161–175.
  • 7. M. H. Pesaran, A. Pick and M. Pranovich, Optimal forecasts in the presence of structural breaks, J. Econometrics, 177 (2013), 134–152.
  • 8. K. Assenmacher-Wesche and M. H. Pesaran, Forecasting the Swiss economy using VECX models: An exercise in forecast combination across models and observation windows, Nat. Inst. Econ. Rev., 203 (2008), 91–108.
  • 9. M. H. Pesaran, T. Schuermann and L. V. Smith, Forecasting economic and financial variables with global VARs, Int. J. Forecasting, 25 (2009), 642–675.
  • 10. A. Schrimpf and Q. Wang, A reappraisal of the leading indicator properties of the yield curve under structural instability, Int. J. Forecasting, 26 (2010), 836–857.
  • 11. D. De Gaetano, Forecast combinations in the presence of structural breaks: Evidence from U.S. equity markets, Math., 6 (2018), 34.
  • 12. M. H. Pesaran and A. Pick, Forecast combination across estimation windows, J. Bus. Econ. Stat., 29 (2011), 307–318.
  • 13. T. E. Clark and M. W. McCracken, Improving forecast accuracy by combining recursive and rolling forecasts, Int. Econ. Rev., 50 (2009), 363–395.
  • 14. D. De Gaetano, Forecast Combinations for Structural Breaks in Volatility: Evidence from BRICS Countries, J. Risk. Financ. Manag., 11 (2018), 64.
  • 15. D. De Gaetano, Forecasting with GARCH models under structural breaks: An approach based on combinations across estimation windows, Commun. Stat. Simulat. Comput., 6 (2018), 1–19.
  • 16. P. R. Hansen, A. Lunde and J. M. Nason, The model confidence set, Econometrica, 79 (2011), 453–497.
  • 17. F. X. Diebold, Modelling the persistence of conditional variance: A comment, Economet. Rev., 5 (1986), 51–56.
  • 18. T. Mikosh and C. Stărică, Nonstationarities in financial time series, the long-range dependence and the IGARCH effects, Rev. Econ. Stat., 86 (2004), 378–390.
  • 19. E. Hillebrand, Neglecting parameter changes in GARCH models, J. Econometrics, 129 (2005), 121–138.
  • 20. S. Hwang and P. L. V. Pereira, Small sample properties of GARCH estimates and persistence, Eur. J. Financ., 12 (2006), 473–494.
  • 21. T. Bollerslev, Generalized Autoregressive Conditional Heteroskedasticity, J. Econometrics, 31 (1986), 307–332.
  • 22. D. B. Nelson, Conditional heteroschedasticity in asset returns: A new approach, Econometrica, 59 (1991), 217–235.
  • 23. L. R. Glosten, R. Jagannathan and D. E. Runkle, On the Relation between the expected value and the volatility of the nominal excess return on stocks, J. Financ., 48 (1993), 1779–1801.
  • 24. C. Forbes, M. Evans, N. Hastings, et al., Statistical distributions, 2nd edition, John Wiley & Sons, 2011.
  • 25. J. Nyblom, Testing for the constancy of parameters over time, J. Am. Stat. Assoc., 84 (1989), 223–230.
  • 26. B. E. Hansen, Tests for parameter instability in regressions with I (1) processes, J. Bus. Econ. Stat., 20 (2002), 45–59.
  • 27. A. Sansó, V. Arragó and J. L. Carrion-i-Silvestre, Testing for change in the unconditional variance of financial time series, Rev. Econ. Financ., 4 (2004), 32–53.
  • 28. C. Inclan and G. C. Tiao, Use of cumulative sums of squares for retrospective detection of changes in variance, J. Am. Stat. Assoc., 89 (1994), 913–923.
  • 29. W. K. Newey and K. D. West, Automatic Lag Selection in Covariance Matrix estimation, Rev. Econ. Stud., 61 (1994), 631–654.
  • 30. G. J. Ross, Modelling financial volatility in the presence of abrupt changes, Physica. A, 392 (2013), 350–360.
  • 31. J. G. MacKinnon, Computing numerical distribution functions in econometrics, in High Performance Computing Systems and Applications, Kluwer, (2000), 455–471.
  • 32. A. J. Patton, Volatility forecast comparison using imperfect volatility proxies, J. Econometrics, 160 (2011), 246–256.


This article has been cited by

  • 1. Davide De Gaetano, A bootstrap bias correction of long run fourth order moment estimation in the CUSUM of squares test, Journal of Statistical Computation and Simulation, 2020, 1, 10.1080/00949655.2020.1711519

Reader Comments

your name: *   your email: *  

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved