Right now, I am analyzing the prediction quality of a dynamic model that has variables with different units (e.g. $x_{1,t}$ is in meters, $x_{2,t}$ is in kilograms etc.). I have discovered a great tool called Mean Absolute Scaled Error: $$ \frac{1}{n}\sum_{t=1}^n\left( \frac{\left| \hat x_{t,i} - x_{t,i} \right|}{\frac{1}{n-1}\sum_{\tau=2}^n \left| x_{\tau,i}-x_{\tau-1,i}\right|} \right) $$ where $i$ is index of variable.

The MASE is denoted as scale-free. I would be curious how to say that the error is large or small. My experience is that $MASE=3$ is not bad, but I would appreciate some more rigorous answer or reference.

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    $\begingroup$ Is this time series data? $\endgroup$ – forecaster Jan 5 '15 at 22:09
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    $\begingroup$ As far as I understand, the magnitude of MASE will differ from case to case not only due to differences in the quality of forecasting methods but also due to the special features of the problem. MASE=3 does not sound impressive, though... Something closer to 1 would be more convincing. (I assume you understand the interpretation of MASE=1.) You may check this question out for another perspective. $\endgroup$ – Richard Hardy Jan 6 '15 at 9:41