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A note on simultaneous calibrated prediction intervals for time series

Author

Listed:
  • Giovanni Fonseca

    (Università di Udine)

  • Federica Giummolè

    (Università Ca’ Foscari Venezia)

  • Paolo Vidoni

    (Università di Udine)

Abstract

This paper deals with simultaneous prediction for time series models. In particular, it presents a simple procedure which gives well-calibrated simultaneous prediction intervals with coverage probability close to the target nominal value. Although the exact computation of the proposed intervals is usually not feasible, an approximation can be easily attained by means of a suitable bootstrap simulation procedure. This new predictive solution is much simpler to compute than those ones already proposed in the literature, based on asymptotic calculations. Applications of the bootstrap calibrated procedure to AR, MA and ARCH models are presented.

Suggested Citation

  • Giovanni Fonseca & Federica Giummolè & Paolo Vidoni, 2021. "A note on simultaneous calibrated prediction intervals for time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 317-330, March.
    • Handle: RePEc:spr:stmapp:v:30:y:2021:i:1:d:10.1007_s10260-020-00526-6
    DOI: 10.1007/s10260-020-00526-6
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    References listed on IDEAS

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    1. Federica Giummolè & Paolo Vidoni, 2010. "Improved prediction limits for a general class of Gaussian models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 483-493, November.
    2. John P. Nolan & Nalini Ravishanker, 2009. "Simultaneous prediction intervals for ARMA processes with stable innovations," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 235-246.
    3. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2008. "On the exact distribution of the maximum of absolutely continuous dependent random variables," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 27-35, January.
    4. Paolo Vidoni, 2004. "Improved prediction intervals for stochastic process models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 137-154, January.
    5. 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.
    6. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    7. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
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