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

Paul Goodwin, Fotios Petropoulos, Rob J Hyndman
(2017) Journal of the Operational Research Society, 68(9), 1082–1084

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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.