Question

Which of the following summary measures for forecast errors does not depend on the units of the forecast variable? a. MFE (mean forecast error) b. MAE (mean absolute error) c. RMSE (root mean square error) d. MAPE (mean absolute percentage error)

Answer 1

Answer:

d. The mean absolute percentage error (MAPE) does not depend on the units of the forecast variable.

Step-by-step explanation:

A forecast error is the difference between the actual or real and the predicted or forecast value of a time series or any other phenomenon of interest. Here “error” does not mean a mistake, it means the unpredictable part of an observation.

There are many different ways to summarize forecast errors in order to provide meaningful information.

Scale-dependent errors. The forecast errors are on the same scale as the data. The two most commonly used scale-dependent measures are based on the absolute errors or squared errors:

$\begin{align*} \text{Mean absolute error: MAE} & = \text{mean}(|e_{t}|),\\ \text{Root mean squared error: RMSE} & = \sqrt{\text{mean}(e_{t}^2)}.\end{align*}$$\text{Mean absolute error: MAE} & = \text{mean}(|e_{t}|),\\ \\\text{Root mean squared error: RMSE} & = \sqrt{\text{mean}(e_{t}^2)}.$

Percentage errors. Percentage errors have the advantage of being unit-free, and so are frequently used to compare forecast performances between data sets. The most commonly used measure is:

$\text{Mean absolute percentage error: MAPE} = \text{mean}(|p_{t}|).$