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Prediction Intervals for ARIMA Models


  • Snyder, Ralph D
  • Ord, J Keith
  • Koehler, Anne B


The problem of constructing prediction intervals for linear time series (ARIMA) models is examined. The aim is to find prediction intervals that incorporate an allowance for sampling error associated with parameter estimates. The effect of constraints on parameters arising from stationarity and invertibility conditions is also incorporated. Two new methods, based on varying degrees of first-order Taylor approximations, are proposed. These are compared in a simulation study to two existing methods, a heuristic approach and the "plug-in" method whereby parameter values are set equal to their maximum likelihood estimates. A comparison of the four methods is also made for quarterly retail sales for 10 Organization for Economic Cooperation and Development countries. The new approaches provide a systematic improvement over existing methods.

Suggested Citation

  • Snyder, Ralph D & Ord, J Keith & Koehler, Anne B, 2001. "Prediction Intervals for ARIMA Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 217-225, April.
  • Handle: RePEc:bes:jnlbes:v:19:y:2001:i:2:p:217-25

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    References listed on IDEAS

    1. Moffitt, Robert, 1992. "Incentive Effects of the U.S. Welfare System: A Review," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 1-61, March.
    2. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    3. Keane, Michael & Moffitt, Robert, 1998. "A Structural Model of Multiple Welfare Program Participation and Labor Supply," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(3), pages 553-589, August.
    4. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September.
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    Cited by:

    1. 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.
    2. 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.
    3. Luis Uzeda, 2016. "State Correlation and Forecasting: A Bayesian Approach Using Unobserved Components Models," ANU Working Papers in Economics and Econometrics 2016-632, Australian National University, College of Business and Economics, School of Economics.
    4. 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.
    5. 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.
    6. 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.
    7. 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

    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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