# How can MASE (Mean Absolute Scaled Error) score value be interpreted for non time series data?

If I have used MASE to calculate non time-series data error (as described by Dr. Rob Hyndman here), how can I know if the score received is good or not? Since it is not a time-series, a random walk naive model is irrelevant here, and the threshold of 1 which is usually used doesn't seems to be a good comparison. Is it correct? if yes - what should be the consideration to decide what score is good or not? if not - why?

BTW it seems that even for time series data, a score of 1 and bellow is not always an achievable target as describe here - so how can you know what is considered to be sufficient?

Based on his textbook for a non-seasonal time series, a useful way to define a scaled error uses naïve forecasts: $$q_{j} = \frac{\displaystyle e_{j}}{\displaystyle\frac{1}{T-1}\sum_{i=1}^T |y_t-y_{t-1}|}$$

Acoording to his answer here, it is possible to scale the data using the mean as the base forecast. If $$e_j$$ denotes a prediction error on the test data, then the scaled errors $$q_j$$ are: $$q_{j} = \frac{\displaystyle e_{j}}{\displaystyle\frac{1}{N}\sum_{i=1}^N |Y_i-\bar{Y}|}$$ where $$y_1,\dots,y_N$$ denotes the training data.

Note here that $$Y_{t-1}$$ is replaced with $$\bar{Y}$$

The MASE compares "your" forecast against a naive benchmark forecast calculated in-sample due to the MASE denominator is calculated in-sample, not in the holdout sample. The MASE is a metric for comparing errors to a user-defined baseline:

$$MASE= mean(|q_{j}|)$$

For interpretation of MSE which is not an easy job please have a look at this earlier thread on interpreting the MASE might be helpful from @Stephan Kolassa

My recommendation:

• Check this answer to not confused about the calculation of MSAE and MAE
• if you have a single series, then the MASE is less informative than the MAE, since the MASE is simply the MAE scaled by a factor that does not depend on the forecast. The MASE makes sense once you have multiple series on different levels, where you can't very well compare "raw" MAEs.

Note: the scaling statistic $$Q$$:

$$\text{MASE}=\text{MAE}/Q$$