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


Paul Goodwin, Fotios Petropoulos, Rob J Hyndman


28 March 2017

Publication details

Journal of the Operational Research Society, 68(9), 1082–1084



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.