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Bootstrap prediction intervals for threshold autoregressive models

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  • Jing, Li

Abstract

This paper examines the performance of prediction intervals based on bootstrap for threshold autoregressive models. We consider four bootstrap methods to account for the variability of estimates, correct the small-sample bias of autoregressive coefficients and allow for heterogeneous errors. Simulation shows that (1) accounting for the sampling variability of estimated threshold values is necessary despite super-consistency, (2) bias-correction leads to better prediction intervals under certain circumstances, and (3) two-sample bootstrap can improve long term forecast when errors are regime-dependent.

Suggested Citation

  • Jing, Li, 2009. "Bootstrap prediction intervals for threshold autoregressive models," MPRA Paper 13086, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:13086
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    References listed on IDEAS

    as
    1. Jae H. Kim, 2004. "Bias-corrected bootstrap prediction regions for vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(2), pages 141-154.
    2. Kim, Jae H, 2001. "Bootstrap-after-Bootstrap Prediction Intervals for Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 117-128, January.
    3. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-144, April.
    4. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    5. Maekawa, Koichi, 1987. "Finite Sample Properties of Several Predictors From an Autoregressive Model," Econometric Theory, Cambridge University Press, vol. 3(3), pages 359-370, June.
    6. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    7. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-135, April.
    8. 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 265-280, July.
    9. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
    10. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    11. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
    12. Grigoletto, Matteo, 1998. "Bootstrap prediction intervals for autoregressions: some alternatives," International Journal of Forecasting, Elsevier, vol. 14(4), pages 447-456, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Bootstrap; Interval Forecasting; Threshold Autoregressive Models; Time Series; Simulation;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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