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Bootstrap Prediction Intervals for Autoregressive Models of Unknown or Infinite Lag Order

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  • Kim, Jae H

Abstract

Recent studies on bootstrap prediction intervals for autoregressive (AR) model provide simulation findings when the lag order is known. In practical applications, however, the AR lag order is unknown or can even be infinite. This paper is concerned with prediction intervals for AR models of unknown or infinite lag order. Akaike's information criterion is used to estimate (approximate) the unknown (infinite) AR lag order. Small-sample properties of bootstrap and asymptotic prediction intervals are compared under both normal and non-normal innovations. Bootstrap prediction intervals are constructed based on the percentile and percentile-t methods, using the standard bootstrap as well as the bootstrap-after-bootstrap. It is found that bootstrap-after-bootstrap prediction intervals show small-sample properties substantially better than other alternatives, especially when the sample size is small and the model has a unit root or near-unit root. Copyright © 2002 by John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:jof:jforec:v:21:y:2002:i:4:p:265-80
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    Cited by:

    1. Anna Staszewska‐Bystrova, 2011. "Bootstrap prediction bands for forecast paths from vector autoregressive models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(8), pages 721-735, December.
    2. Jing Li, 2021. "Block bootstrap prediction intervals for parsimonious first‐order vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(3), pages 512-527, April.
    3. Clements, Michael P. & Kim, Jae H., 2007. "Bootstrap prediction intervals for autoregressive time series," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3580-3594, April.
    4. Jing, Li, 2009. "Bootstrap prediction intervals for threshold autoregressive models," MPRA Paper 13086, University Library of Munich, Germany.
    5. Anna Staszewska-Bystrova, 2009. "Bootstrap Confidence Bands for Forecast Paths," Working Papers 024, COMISEF.
    6. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332, April.
    7. Kim, Jae H., 2004. "Bootstrap prediction intervals for autoregression using asymptotically mean-unbiased estimators," International Journal of Forecasting, Elsevier, vol. 20(1), pages 85-97.
    8. Li, Jing, 2011. "Bootstrap prediction intervals for SETAR models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 320-332.

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