The Mean Absolute Scaled Error (MASE) was proposed by Hyndman & Koehler (2006, *International Journal of Forecasting*) as a scale free accuracy measure for point forecasts. It is defined as the ratio of the MAE to the one-step MAE achieved *in-sample* (this is frequently gotten wrong) by a simple benchmark method (often the naive random walk forecast).
For historical data $y_1, \dots, y_T$ and forecasts $\hat{y}_{T+1}, \dots, \hat{y}_{T+H}$, the MASE is defined as
$$\text{MASE}:=\frac{\frac{1}{H}\sum_{h=1}^H|y_{T+h}-\hat{y}_{T+h}|}{Q}$$
The numerator is the Mean Absolute Error (MAE) of our forecasts while the denominator, $Q$, is a scaling factor equal to the MAE based on in-sample one-step benchmark forecasts. For non-seasonal data, the benchmark method is often the naive random walk so that
$$Q = \frac{1}{T-1}\sum_{t=2}^T|y_t-y_{t-1}|.$$
For seasonal data, the benchmark method is often the seasonal naive method, so that
$$Q = \frac{1}{T-m}\sum_{t=m+1}^T|y_t-y_{t-m}|$$
where $m$ is the period of seasonality.
An open-access non-technical introduction is provided by Hyndman and Athanasopoulos (2014, Section 2.5). Hyndman (2006, Foresight) is a longer, non-gated and non-technical introduction to the MASE in the context of intermittent demand forecasting. However, note that Kolassa (2016, International Journal of Forecasting) notes that the MASE is explicitly not suitable to assess forecasts for intermittent data.
Alternatives to the MASE as a point forecast accuracy measure include the mape, the mae and the mse.
