Which measure of error calculates the average absolute value of the actual forecast error?

The mean absolute percentage error (MAPE) is one of the most widely used measures of forecast accuracy, due to its advantages of scale-independency and interpretability. However, MAPE has the significant disadvantage that it produces infinite or undefined values for zero or close-to-zero actual values. In order to address this issue in MAPE, we propose a new measure of forecast accuracy called the mean arctangent absolute percentage error (MAAPE). MAAPE has been developed through looking at MAPE from a different angle. In essence, MAAPE is a slope as an angle, while MAPE is a slope as a ratio, considering a triangle with adjacent and opposite sides that are equal to an actual value and the difference between the actual and forecast values, respectively. MAAPE inherently preserves the philosophy of MAPE, overcoming the problem of division by zero by using bounded influences for outliers in a fundamental manner through considering the ratio as an angle instead of a slope. The theoretical properties of MAAPE are investigated, and the practical advantages are demonstrated using both simulated and real-life data.

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Keywords

Accuracy measure

Forecast evaluation

Intermittent demand

MAPE

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Sungil Kim, who is currently working as a data scientist for Samsung SDS, received his Ph.D. degree in Industrial Engineering, M.S. degrees in Industrial Engineering and Statistics from the Georgia Institute of Technology, and B.S. degree in Industrial Engineering from Yonsei University. His major research interests are in the areas of demand forecasting, data mining and machine learning, multi-level multi-scale modeling, and business analytics.

Heeyoung Kim is currently an assistant professor in Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology (KAIST). She received her Ph.D. degree in Industrial Engineering from the Georgia Institute of Technology, and B.S. and M.S. degrees in Industrial Engineering from Korea Advanced Institute of Science and Technology (KAIST). Her research interests are in the areas of data mining and machine learning, nonparametric statistical methods, and business applications with spatio-temporal data analysis.

MAPE stands for Mean Absolute Percent Error - Bias refers to persistent forecast error - Bias is a component of total calculated forecast error - Bias refers to consistent under-forecasting or over-forecasting - MAPE can be misinterpreted and miscalculated, so use caution in the interpretation.

Accurate and timely demand plans are a vital component of a manufacturing supply chain. Inaccurate demand forecasts typically would result in supply imbalances when it comes to meeting customer demand. Forecast accuracy at the SKU level is critical for proper allocation of resources.

When we talk about forecast accuracy in the supply chain, we typically have one measure in mind namely, the Mean Absolute Percent Error or MAPE. However, there is a lot of confusion between Academic Statisticians and corporate Supply Chain Planners in interpreting this metric. Most academics define MAPE as an average of percentage errors over a number of products. Whether it is erroneous is subject to debate. However, this interpretation of MAPE is useless from a manufacturing supply chain perspective. The following is a discussion of forecast error and an elegant method to calculate meaningful MAPE.

Definition of Forecast Error

Forecast Error is the deviation of the Actual from the forecasted quantity.

• Error = absolute value of {(Actual – Forecast) = |(A - F)|
• Error (%) = |(A – F)|/A

We take absolute values because the magnitude of the error is more important than the direction of the error.

The Forecast Error can be bigger than Actual or Forecast but NOT both. Error above 100% implies a zero forecast accuracy or a very inaccurate forecast.

• Error close to 0% => Increasing forecast accuracy
• Forecast Accuracy is the converse of Error
• Accuracy (%) = 1 – Error (%)

How do you define Forecast Accuracy?

What is the impact of Large Forecast Errors? Is Negative accuracy meaningful?
Regardless of huge errors, and errors much higher than 100% of the Actuals or Forecast, we interpret accuracy a number between 0% and 100%. Either a forecast is perfect or relative accurate or inaccurate or just plain incorrect. So we constrain Accuracy to be between 0 and 100%.

More formally, Forecast Accuracy is a measure of how close the actuals are to the forecasted quantity.

Which measure of error calculates the average error in the forecast using absolute values?

Which measure of error calculates the average absolute value of the actual forecast error multiple choice question RSFE TS MAPE MAD?

Which of the following is the measure of forecast error?

What is MAPE a measure of?