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Bootstrap prediction intervals for SETAR models

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  • Li, Jing

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.

Suggested Citation

  • Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332.
  • Handle: RePEc:eee:intfor:v:27:y:2011:i:2:p:320-332
    DOI: 10.1016/j.ijforecast.2010.01.013
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    5. Anna Staszewska-Bystrova & Peter Winker, 2016. "Improved bootstrap prediction intervals for SETAR models," Statistical Papers, Springer, vol. 57(1), pages 89-98, March.
    6. 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.
    7. Grabowski Daniel & Winker Peter & Staszewska-Bystrova Anna, 2017. "Generating prediction bands for path forecasts from SETAR models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(5), pages 1-18, December.
    8. Anna Staszewska-Bystrova & Peter Winker, 2016. "Improved bootstrap prediction intervals for SETAR models," Statistical Papers, Springer, vol. 57(1), pages 89-98, March.

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