Root Mean Squared Error (RMSE)

RMSE summarises how far forecasts typically are from actual values, in the same units as the data. A lower RMSE indicates more accurate forecasts.

For example, if three forecasts have errors of 10, minus 20 and 30, the squared errors are 100, 400 and 900. Their average is about 466.7, and the square root is about 21.6. The RMSE is about 21.6.

Because errors are squared before averaging, RMSE gives much more weight to large errors than small ones. This makes it useful when large errors are particularly costly, but it also means a few big misses can dominate the result. By comparison, the mean absolute error of the same three forecasts is 20.

RMSE is widely used to compare forecasting models, evaluate machine learning models and measure the accuracy of economic and financial forecasts. Because it is expressed in the units of the data, it cannot be compared across series of different scales, for which percentage measures such as mean absolute percentage error may be more suitable.