An MSE statistic for comparing forecast accuracy across series

Most forecasters agree that, for a single time series, mean squared error (MSE) is a useful statistic for comparing forecast accuracy under quadratic loss. There is little agreement, however, on how to use MSE for assessing overall accuracy across many series. This paper proposes an MSE statistic, log mean squared error ratio (LMR), designed for this purpose. The theoretical behavior of forecast MSE is characterized by a multiplicative model containing parameters that measure characteristics of the time series and how the forecasting model interacts with the series. LMR is the natural product of transforming these multiplicative effects to an additive relationship. An example demonstrates that LMR, averaged over series, consistently ranks the techniques for overall accuracy.