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On forecasting SETAR processes

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  • De Gooijer, Jan G.
  • De Bruin, Paul T.

Abstract

Suppose a time series {Yt} is generated by a first-order stationary self-exciting threshold autoregressive (SETAR) model with Gaussian innovations. The minimum mean squared error h-step ahead forecast for h> 2 involves a sequence of complicated numerical integrations and closed-form expressions are very difficult or even impossible to obtain. In this paper we derive explicit approximate expressions for E[Yt+hYs; s [less-than-or-equals, slant] t] and Var[Yt+hYs; s [less-than-or-equals, slant] t] (h> 2) for various SETAR models. The approximations are reasonably accurate as compared with alternative methods based on numerical integration and Monte Carlo experiments.

Suggested Citation

  • De Gooijer, Jan G. & De Bruin, Paul T., 1998. "On forecasting SETAR processes," Statistics & Probability Letters, Elsevier, vol. 37(1), pages 7-14, January.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:1:p:7-14
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    References listed on IDEAS

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    1. M. S. Al‐Qassam & J. A. Lane, 1989. "Forecasting Exponential Autoregressive Models Of Order 1," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(2), pages 95-113, March.
    2. John. Pemberton, 1987. "Exact Least Squares Multi‐Step Prediction From Nonlinear Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(4), pages 443-448, July.
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    Cited by:

    1. Ramazan Gencay & Ege Yazgan, 2017. "When Are Wavelets Useful Forecasters?," Working Papers 1704, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    2. Mehmet Pinar & Thanasis Stengos & M. Ege Yazgan, 2012. "Is there an optimal forecast combination? A stochastic dominance approach applied to the forecast combination puzzle," Working Papers 1206, University of Guelph, Department of Economics and Finance.
    3. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 8, pages 413-457, Elsevier.
    4. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    5. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654.
    6. Dueker, Michael J. & Sola, Martin & Spagnolo, Fabio, 2007. "Contemporaneous threshold autoregressive models: Estimation, testing and forecasting," Journal of Econometrics, Elsevier, vol. 141(2), pages 517-547, December.
    7. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332.
    8. Mehmet Pinar & Thanasis Stengos & M. Ege Yazgan, 2018. "Quantile forecast combination using stochastic dominance," Empirical Economics, Springer, vol. 55(4), pages 1717-1755, December.
    9. Hui Feng & Jia Liu, 2003. "A SETAR model for Canadian GDP: non-linearities and forecast comparisons," Applied Economics, Taylor & Francis Journals, vol. 35(18), pages 1957-1964.
    10. Amendola, Alessandra & Christian, Francq, 2009. "Concepts and tools for nonlinear time series modelling," MPRA Paper 15140, University Library of Munich, Germany.
    11. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332, April.
    12. De Gooijer, Jan G. & Ray, Bonnie K., 2003. "Modeling vector nonlinear time series using POLYMARS," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 73-90, February.
    13. Perez-Rodriguez, Jorge V. & Torra, Salvador & Andrada-Felix, Julian, 2005. "STAR and ANN models: forecasting performance on the Spanish "Ibex-35" stock index," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 490-509, June.
    14. Paulo M.M. Rodrigues & Nazarii Salish, 2011. "Modeling and Forecasting Interval Time Series with Threshold Models: An Application to S&P500 Index Returns," Working Papers w201128, Banco de Portugal, Economics and Research Department.
    15. Harun Özkan & M. Yazgan, 2015. "Is forecasting inflation easier under inflation targeting?," Empirical Economics, Springer, vol. 48(2), pages 609-626, March.

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