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Abstract

This paper considers four methods for obtaining bootstrap prediction intervals (BPIs) for the self-exciting threshold autoregressive (SETAR) model. Method 1 ignores the sampling variability of the threshold parameter estimator. Method 2 corrects the finite sample biases of the autoregressive coefficient estimators before constructing BPIs. Method 3 takes into account the sampling variability of both the autoregressive coefficient estimators and the threshold parameter estimator. Method 4 resamples the residuals in each regime separately. A Monte Carlo experiment shows that (1) accounting for the sampling variability of the threshold parameter estimator is necessary, despite its super-consistency; (2) correcting the small-sample biases of the autoregressive parameter estimators improves the small-sample properties of bootstrap prediction intervals under certain circumstances; and (3) the two-sample bootstrap can improve the long-term forecasts when the error terms are regime-dependent.

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File URL: http://www.sciencedirect.com/science/article/B6V92-4YX0BGH-1/2/33e4dc855484c3864df35efa3867b928
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Bibliographic Info

Article provided by Elsevier in its journal International Journal of Forecasting.

Volume (Year): 27 (2011)
Issue (Month): 2 (April)
Pages: 320-332

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Handle: RePEc:eee:intfor:v:27:y::i:2:p:320-332

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Web page: http://www.elsevier.com/locate/ijforecast

Related research

Keywords: Bootstrap Interval forecasting SETAR models Time series Simulation;

References

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1. Clements, Michael P. & Smith, Jeremy, 1997. "The performance of alternative forecasting methods for SETAR models," International Journal of Forecasting, Elsevier, vol. 13(4), pages 463-475, December.
2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
   
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   • Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
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   • Hansen,B.E., 1998. "The grid bootstrap and the autoregressive model," Working papers 26, Wisconsin Madison - Social Systems.
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11. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
    
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12. Clements, Michael P & Smith, Jeremy, 1999. "A Monte Carlo Study of the Forecasting Performance of Empirical SETAR Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 123-41, March-Apr.
    
    • Clements, Michael P & Smith, Jeremy, 1996. "A Monte Carlo Study of the Forecasting Performance of Empirical Setar Models," The Warwick Economics Research Paper Series (TWERPS) 464, University of Warwick, Department of Economics.
13. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    
    • Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
14. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-35, April.
15. P. Siklos, W. Enders & B. Falk, 2006. "A Threshold Model of Real US GDP and the Problem of Constructing Confidence Intervals in TAR Models," Working Papers eg0052, Wilfrid Laurier University, Department of Economics, revised 2006.
    
    • Walter Enders & Barry L. Falk & Pierre Siklos, 2007. "A Threshold Model of Real U.S. GDP and the Problem of Constructing Confidence Intervals in TAR Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 11(3), pages 4.
16. Bruce E. Hansen, 1997. "Inference in TAR Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(1), pages 1.
    
    • Tom Doan, . "THRESHTEST: RATS procedure to perform Hansen's Test for Threshold Break," Statistical Software Components RTS00210, Boston College Department of Economics.
17. Kim, Jae H, 2002. "Bootstrap Prediction Intervals for Autoregressive Models of Unknown or Infinite Lag Order," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(4), pages 265-80, July.
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19. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
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Cited by:

1. Frédérique Bec & Othman Bouabdallah & Laurent Ferrara, 2011. "The European Way Out of Recessions," THEMA Working Papers 2011-23, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
   
   • Bec, F. & Bouabdallah, O. & Ferrara, L., 2012. "The European way out of recession," Working papers 360, Banque de France.

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