Measures of accuracy

The most common accuracy measure is the Root Mean Square Error (RMSE):

which measures the distance between the forecast and the verifying analysis or observation. The RMSE is negatively orientated, i.e. increasing numerical values indicate increasing “failure”.

The mean absolute error:

is also negatively orientated. Due to its quadratic nature, the RMSE penalizes large errors more than the non-quadratic MAE and thus takeshigher numerical values. This might be one reason why MAE is sometimes preferred, although the practical consequences of forecast errors are probably better represented by the RMSE. We will concentrate on the RMSE, or rather the squared version, the mean square error:

which is more convenient to analyse mathematically.