Using Naïve Forecasts to Assess Limits to Forecast Accuracy and the Quality of Fit of Forecasts to Time Series Data

Naive 1 forecasts are often used as a benchmark when assessing the accuracy of a set of forecasts. A ratio is obtained to show the upper bound of a forecasting method's accuracy relative to naive 1 forecasts when the mean squared error is used to measure accuracy. Formulae for the ratio are presented for several exemplar time series processes. The practical use of the ratio as a warning that forecasts have failed to adequately filter the time series signal from the noise is demonstrated.