Question

Which one of the following is NOT a measure of forecast error?

• A. Mean absolute deviation (MAD)
• B. Mean squared error (MSE)
• C. Mean absolute percent error (MAPE)
• D. Mean sum product error (MSPE)

Hint:

MAD, MSE, and MAPE are common measures of forecast error. MSPE is not a standard metric used in forecasting.

Answer 1

The Correct Option is D

In forecasting, we use various measures to assess the accuracy of our predictions. The following are commonly used measures of forecast error: 1. Mean Absolute Deviation (MAD): This is the average of the absolute errors between the forecasted and actual values. It gives us an indication of the average magnitude of errors in the forecast, irrespective of direction. \[ \text{MAD} = \frac{1}{n} \sum_{i=1}^{n} |Y_i - \hat{Y}_i| \] where \( Y_i \) is the actual value, and \( \hat{Y}_i \) is the forecasted value. 2. Mean Squared Error (MSE): This is the average of the squared differences between the forecasted and actual values. It penalizes larger errors more than MAD due to the squaring term. \[ \text{MSE} = \frac{1}{n} \sum_{i=1}^{n} (Y_i - \hat{Y}_i)^2 \] 3. Mean Absolute Percent Error (MAPE): This is the average of the absolute percentage errors. It is useful when you want to understand the error relative to the size of the forecasted values. \[ \text{MAPE} = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{Y_i - \hat{Y}_i}{Y_i} \right| \times 100 \] The Mean Sum Product Error (MSPE), however, is not a standard or commonly used measure of forecast error. It may refer to a different concept, but it is not typically used for evaluating forecast accuracy in the way the other metrics are. Thus, MSPE is not a measure of forecast error. Thus, the correct answer is (D).