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Improved prediction intervals for stochastic process models

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  • Paolo Vidoni

Abstract

. This paper reviews some recent results on the construction of improved prediction limits for time series models and presents a simple solution based on a fully conditional approach. A prediction limit, expressed as a modification of the estimative one, is obtained so that its conditional and unconditional coverage probability equals the target value to third‐order accuracy. Although the specification of the ancillary statistic is not required, it respects the conditionality principle, to the relevant order of approximation. Moreover, the corresponding predictive density is specified in a relatively simple closed form. Simple examples show the usefulness of this conditional approach to prediction.

Suggested Citation

  • Paolo Vidoni, 2004. "Improved prediction intervals for stochastic process models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 137-154, January.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:1:p:137-154
    DOI: 10.1111/j.1467-9892.2004.00341.x
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    References listed on IDEAS

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    1. Paul Kabaila, 1999. "The Relevance Property For Prediction Intervals," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(6), pages 655-662, November.
    2. Paul Kabaila, 1993. "On Bootstrap Predictive Inference For Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(5), pages 473-484, September.
    3. 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.
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    Cited by:

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    2. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org, revised Jan 2019.
    3. 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.
    4. 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.
    5. Kabaila, Paul & Syuhada, Khreshna, 2010. "The asymptotic efficiency of improved prediction intervals," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1348-1353, September.
    6. 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.
    7. Mulubrhan G. Haile & Lingling Zhang & David J. Olive, 2024. "Predicting Random Walks and a Data-Splitting Prediction Region," Stats, MDPI, vol. 7(1), pages 1-11, January.
    8. 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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