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Improved multivariate prediction regions for Markov process models

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  • Paolo Vidoni

    (University of Udine)

Abstract

This paper concerns the specification of multivariate prediction regions which may be useful in time series applications whenever we aim at considering not just one single forecast but a group of consecutive forecasts. We review a general result on improved multivariate prediction and we use it in order to calculate conditional prediction intervals for Markov process models so that the associated coverage probability turns out to be close to the target value. This improved solution is asymptotically superior to the estimative one, which is simpler but it may lead to unreliable predictive conclusions. An application to general autoregressive models is presented, focusing in particular on AR and ARCH models.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:26:y:2017:i:1:d:10.1007_s10260-016-0362-y
    DOI: 10.1007/s10260-016-0362-y
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    References listed on IDEAS

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    1. Corcuera, José M., 2008. "Approximate predictive pivots for autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2685-2691, November.
    2. Òscar Jordà & Massimiliano Marcellino, 2010. "Path forecast evaluation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 635-662.
    3. D. Concordet & R. Servien, 2014. "Individual prediction regions for multivariate longitudinal data with small samples," Biometrics, The International Biometric Society, vol. 70(3), pages 629-638, September.
    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. Michael Wolf & Dan Wunderli, 2012. "Bootstrap joint prediction regions," ECON - Working Papers 064, Department of Economics - University of Zurich, revised May 2013.
    6. J. F. Lawless & Marc Fredette, 2005. "Frequentist prediction intervals and predictive distributions," Biometrika, Biometrika Trust, vol. 92(3), pages 529-542, September.
    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.
    8. 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.
    9. Vidoni, Paolo, 2015. "Calibrated multivariate distributions for improved conditional prediction," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 16-25.
    10. Masao Ueki & Kaoru Fueda, 2007. "Adjusting estimative prediction limits," Biometrika, Biometrika Trust, vol. 94(2), pages 509-511.
    11. Wang, Wan-Lun & Fan, Tsai-Hung, 2010. "ECM-based maximum likelihood inference for multivariate linear mixed models with autoregressive errors," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1328-1341, 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.

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