, Volume 25, Issue 1, pp 77–93 | Cite as

Conditions for the optimality of exponential smoothing forecast procedures

  • J. Ledolter
  • G. E. P. Box


Exponential smoothing procedures, in particular those recommended byBrown [1962] are used extensively in many areas of economics, business and engineering. It is shown in this paper that:
  1. i)

    Brown's forecasting procedures are optimal in terms of achieving minimum mean square error forecasts only if the underlying stochastic process is included in a limited subclass of ARIMA (p, d, q) processes. Hence, it is shown what assumptions are made when using these procedures.

  2. ii)

    The implication of point (i) is that the users ofBrown's procedures tacitly assume that the stochastic processes which occur in the real world are from the particular restricted subclass of ARIMA (p, d, q) processes. No reason can be found why these particular models should occur more frequently than others.

  3. iii)

    It is further shown that even if a stochastic process which would lead toBrown's model occurred, the actual methods used for making the forecasts are clumsy and much simpler procedures can be employed.



Real World Stochastic Process Probability Theory Economic Theory Error Forecast 
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Copyright information

© Physica-Verlag Rudolf Liebing KG 1978

Authors and Affiliations

  • J. Ledolter
    • 1
  • G. E. P. Box
    • 2
  1. 1.International Institute for Applied Systems AnalysisLaxenburgAustria
  2. 2.Department of StatisticsUniversity of WisconsinMadisonUSA

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