Correspondence on the selection of error measures for comparisons among forecasting methods

Clements and Hendry proposed the Generalized Forecast Error Second Moment (GFESM) as an improvement to the Mean Square Error in comparing forecasting performance across data series. They based their conclusion on the fact that rankings based on GFESM remain unaltered if the series are linearly transformed. This paper argues that this evaluation ignores other important criteria. Also, their conclusions were illustrated by a simulation study whose relationship to real data was not obvious. Thirdly, prior empirical studies show that the mean square error is an inappropriate measure to serve as a basis for comparison. This undermines the claims made for the GFESM.