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Forecasting time series with sieve bootstrap

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

Abstract

In this paper we consider bootstrap methods for constructing nonparametric prediction intervals for a general class of linear processes. Our approach uses the sieve bootstrap procedure of Biihlmann (1997) based on residual resampling from an autoregressive approximation to the given process. We show that the sieve bootstrap provides consistent estimators of the conditional distribution of future values given the observed data, assuming that the order of the autoregressive approximation increases with the sample size at a suitable rate and some restrictions about polynomial decay of the coefficients ~ j t:o of the process MA(oo) representation. We present a Monte Carlo study comparing the finite sample properties of the sieve bootstrap with those of alternative methods. Finally, we illustrate the performance of the proposed method with real data examples.

Suggested Citation

  • Alonso Fernández, Andrés Modesto & Peña, Daniel & Romo, Juan, 2000. "Forecasting time series with sieve bootstrap," DES - Working Papers. Statistics and Econometrics. WS 9858, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:9858
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    References listed on IDEAS

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    1. Matteo Grigoletto, 1998. "Bootstrap prediction intervals for autoregressive models fitted to non-autoregressive processes," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(3), pages 285-295, December.
    2. R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 577-602, September.
    3. 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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    1. Alonso, Andrés M. & Peña, Daniel & Romo, Juan, 2003. "On sieve bootstrap prediction intervals," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 13-20, October.

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