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Prediction Intervals for Arima Models

Author

Listed:
  • Snyder, R.D.
  • Ord, J.K.
  • Koehler, A.B.

Abstract

The problem of constructing prediction intervals for linear time series (ARIMA) models is examined. The aim is to find prediction intervals which incorporate an allowance for sampling error associated with parameter estimates. The effect of constraints on parameters arising from stationary and invertibility conditions is also incorporated. Two new methods, based to varying degrees on first-order Taylor approximations, are proposed.

Suggested Citation

  • Snyder, R.D. & Ord, J.K. & Koehler, A.B., 1997. "Prediction Intervals for Arima Models," Monash Econometrics and Business Statistics Working Papers 8/97, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:1997-8
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    Citations

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    Cited by:

    1. Rob Hyndman & Muhammad Akram & Blyth Archibald, 2008. "The admissible parameter space for exponential smoothing models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 407-426, June.
    2. J Keith Ord & Ralph D Snyder & Anne B Koehler & Rob J Hyndman & Mark Leeds, 2005. "Time Series Forecasting: The Case for the Single Source of Error State Space," Monash Econometrics and Business Statistics Working Papers 7/05, Monash University, Department of Econometrics and Business Statistics.
    3. Forbes, C.S. & Snyder, R.D. & Shami, R.S., 2000. "Bayesian Exponential Smoothing," Monash Econometrics and Business Statistics Working Papers 7/00, Monash University, Department of Econometrics and Business Statistics.
    4. Merten, Michael & Rücker, Fabian & Schoeneberger, Ilka & Sauer, Dirk Uwe, 2020. "Automatic frequency restoration reserve market prediction: Methodology and comparison of various approaches," Applied Energy, Elsevier, vol. 268(C).
    5. Koehler, Anne B. & Snyder, Ralph D. & Ord, J. Keith & Beaumont, Adrian, 2012. "A study of outliers in the exponential smoothing approach to forecasting," International Journal of Forecasting, Elsevier, vol. 28(2), pages 477-484.
    6. Luis Uzeda, 2022. "State Correlation and Forecasting: A Bayesian Approach Using Unobserved Components Models," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 25-53, Emerald Group Publishing Limited.
    7. Ralph D. Snyder, 2004. "Exponential Smoothing: A Prediction Error Decomposition Principle," Monash Econometrics and Business Statistics Working Papers 15/04, Monash University, Department of Econometrics and Business Statistics.
    8. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.

    More about this item

    Keywords

    STATISTICS ; ECONOMETRICS;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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