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Simultaneous prediction intervals for ARMA processes with stable innovations

Author

Listed:
  • John P. Nolan

    (Math|Stat Department, American University, Washington, DC, USA)

  • Nalini Ravishanker

    (Department of Statistics, University of Connecticut, Storrs, CT, USA)

Abstract

We describe a method for calculating simultaneous prediction intervals for ARMA times series with heavy-tailed stable innovations. The spectral measure of the vector of prediction errors is shown to be discrete. Direct computation of high-dimensional stable probabilities is not feasible, but we show that Monte Carlo estimates of the interval width is practical. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:jof:jforec:v:28:y:2009:i:3:p:235-246
    DOI: 10.1002/for.1102
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    References listed on IDEAS

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    1. Cline, Daren B. H. & Brockwell, Peter J., 1985. "Linear prediction of ARMA processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 281-296, April.
    2. Zuqiang Qiou & Nalini Ravishanker, 1998. "Bayesian Inference for Time Series with Stable Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(2), pages 235-249, March.
    3. Glaz, Joseph & Ravishanker, Nalini, 1991. "Simultaneous prediction intervals for multiple forecasts based on Bonferroni and product-type inequalities," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 57-63, July.
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    Cited by:

    1. Dag Kolsrud, 2015. "A Time‐Simultaneous Prediction Box for a Multivariate Time Series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(8), pages 675-693, December.
    2. 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.

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