Journal of the Operational Research Society

, Volume 68, Issue 9, pp 1082–1084 | Cite as

A note on upper bounds for forecast-value-added relative to naïve forecasts

  • Paul Goodwin
  • Fotios Petropoulos
  • Rob J. Hyndman


In forecast value added analysis, the accuracy of relatively sophisticated forecasting methods is compared to that of naïve 1 forecasts to see whether the extra costs and effort of implementing them are justified. In this note, we derive a ratio that indicates the upper bound of a forecasting method’s accuracy relative to naïve 1 forecasts when the mean squared error is used to measure one-period-ahead accuracy. The ratio is applicable when a series is stationary or when its first differences are stationary. Formulae for the ratio are presented for several exemplar time series processes.


forecasting forecast accuracy ARIMA models 


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Copyright information

© The Operational Research Society 2017

Authors and Affiliations

  • Paul Goodwin
    • 1
  • Fotios Petropoulos
    • 1
  • Rob J. Hyndman
    • 2
  1. 1.The Management SchoolUniversity of BathBathUK
  2. 2.Department of Econometrics and Business StatisticsMonash UniversityClaytonAustralia

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