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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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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Ramazan Gencay & Ege Yazgan, 2017. "When Are Wavelets Useful Forecasters?," Working Papers 1704, The Center for Financial Studies (CEFIS), Istanbul Bilgi University.
    4. 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.
    5. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, Elsevier.
    6. 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.
    7. Amendola, Alessandra & Christian, Francq, 2009. "Concepts and tools for nonlinear time series modelling," MPRA Paper 15140, University Library of Munich, Germany.
    8. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332, April.
    9. 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.
    10. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332.
    11. 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.
    12. 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.
    13. 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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