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Introducing model uncertainty in time series bootstrap

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  • Alonso Fernández, Andrés Modesto
  • Peña, Daniel
  • Romo, Juan

Abstract

It is common in parametric bootstrap to select the model from the data, and then treat it as it were the true model. Kilian (1998) have shown that ignoring the model uncertainty may seriously undermine the coverage accuracy of bootstrap confidence intervals for impulse response estimates which are closely related with multi-step-ahead prediction intervals. In this paper, we propose different ways of introducing the model selection step in the resampling algorithm. We present a Monte Carlo study comparing the finite sample properties of the proposed method with those of alternative methods in the case of prediction intervals.

Suggested Citation

  • Alonso Fernández, Andrés Modesto & Peña, Daniel & Romo, Juan, 2001. "Introducing model uncertainty in time series bootstrap," DES - Working Papers. Statistics and Econometrics. WS ws011409, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws011409
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    References listed on IDEAS

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    1. Alonso Fernández, Andrés Modesto & Peña, Daniel & Romo, Juan, 2000. "Resampling time series by missing values techniques," DES - Working Papers. Statistics and Econometrics. WS 9923, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. B. M. Pötscher, 1990. "Estimation Of Autoregressive Moving‐Average Order Given An Infinite Number Of Models And Approximation Of Spectral Densities," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(2), pages 165-179, March.
    3. Masarotto, Guido, 1990. "Bootstrap prediction intervals for autoregressions," International Journal of Forecasting, Elsevier, vol. 6(2), pages 229-239, July.
    4. R. J. Bhansali, 1983. "A Simulation Study of Autoregressive and Window Estimators of the Inverse Correlation Function," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 141-149, June.
    5. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
    6. Lutz Kilian, 1998. "Accounting for Lag Order Uncertainty in Autoregressions: the Endogenous Lag Order Bootstrap Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(5), pages 531-548, September.
    7. Grigoletto, Matteo, 1998. "Bootstrap prediction intervals for autoregressions: some alternatives," International Journal of Forecasting, Elsevier, vol. 14(4), pages 447-456, December.
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