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A simple procedure for computing improved prediction intervals for autoregressive models

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  • Paolo Vidoni

Abstract

. This article concerns the construction of prediction intervals for time series models. The estimative or plug‐in solution is usually not entirely adequate, since the (conditional) coverage probability may differ substantially from the nominal value. Prediction intervals with improved (conditional) coverage probability can be defined by adjusting the estimative ones, using rather complicated asymptotic procedures or suitable simulation techniques. This article extends to Markov process models a recent result by Vidoni, which defines a relatively simple predictive distribution function, giving improved prediction limits as quantiles. This new solution is fruitfully considered in the challenging context of prediction for time‐series models, with particular regard to AR and ARCH processes.

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  • Paolo Vidoni, 2009. "A simple procedure for computing improved prediction intervals for autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(6), pages 577-590, November.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:6:p:577-590
    DOI: 10.1111/j.1467-9892.2009.00626.x
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    References listed on IDEAS

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    1. Paolo Vidoni, 2009. "Improved Prediction Intervals and Distribution Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 735-748, December.
    2. Paul Kabaila, 1999. "The Relevance Property For Prediction Intervals," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(6), pages 655-662, November.
    3. Paolo Vidoni, 2004. "Improved prediction intervals for stochastic process models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 137-154, January.
    4. J. F. Lawless & Marc Fredette, 2005. "Frequentist prediction intervals and predictive distributions," Biometrika, Biometrika Trust, vol. 92(3), pages 529-542, September.
    5. Paul Kabaila, 1993. "On Bootstrap Predictive Inference For Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 473-484, September.
    6. Phillips, Peter C. B., 1979. "The sampling distribution of forecasts from a first-order autoregression," Journal of Econometrics, Elsevier, vol. 9(3), pages 241-261, February.
    7. Paul Kabaila & Zhisong He, 2004. "The adjustment of prediction intervals to account for errors in parameter estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 351-358, May.
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    Cited by:

    1. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org, revised Jan 2019.
    2. Paolo Vidoni, 2009. "Improved Prediction Intervals and Distribution Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 735-748, December.
    3. Kabaila, Paul & Syuhada, Khreshna, 2010. "The asymptotic efficiency of improved prediction intervals," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1348-1353, September.
    4. Paolo Vidoni, 2017. "Improved multivariate prediction regions for Markov process models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 1-18, March.

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