The mean absolute deviation (MAD) of a forecast is the average of the absolute differences between the forecasted values and the actual values. It measures the average magnitude of the errors in a set of forecasts, without considering their direction (i.e., whether the forecasts are over or under the actual values).
Understanding Mean Absolute Deviation (MAD)
MAD is a crucial metric for evaluating the accuracy of forecasting models. A lower MAD indicates that the forecast is generally closer to the actual values, suggesting better accuracy. It provides a straightforward and easily interpretable measure of forecast error.
Calculating MAD
The formula for calculating MAD is as follows:
MAD = Σ |Actual - Forecast| / N
Where:
- Σ represents the sum of the absolute differences.
- |Actual - Forecast| represents the absolute value of the difference between the actual value and the forecasted value for each period.
- N represents the number of periods.
Steps for Calculation:
- Calculate the forecast error: Subtract the forecast value from the actual value for each period.
- Take the absolute value of each error: This removes the negative signs, so you're only concerned with the magnitude of the error.
- Sum the absolute errors: Add up all the absolute error values.
- Divide by the number of periods: This gives you the average absolute error.
Example
Let's say we have the following actual and forecasted demand for a product over five months:
| Month | Actual Demand | Forecasted Demand |
|---|---|---|
| 1 | 100 | 90 |
| 2 | 120 | 110 |
| 3 | 110 | 125 |
| 4 | 95 | 85 |
| 5 | 130 | 140 |
Calculation:
- Absolute Errors: |100-90| = 10, |120-110| = 10, |110-125| = 15, |95-85| = 10, |130-140| = 10
- Sum of Absolute Errors: 10 + 10 + 15 + 10 + 10 = 55
- MAD: 55 / 5 = 11
Therefore, the mean absolute deviation (MAD) for this forecast is 11. On average, the forecast deviates from the actual demand by 11 units per month.
Importance of MAD
- Simple to understand: MAD is easy to calculate and interpret, making it accessible to a wide audience.
- Useful for comparison: It allows you to compare the accuracy of different forecasting methods. A lower MAD generally indicates a more accurate forecasting model.
- Focuses on magnitude: MAD emphasizes the size of the errors, which is important in many real-world scenarios.
Limitations
While useful, MAD has limitations:
- Equal weighting: It treats all errors equally, regardless of their size. Other metrics, like Mean Squared Error (MSE), give more weight to larger errors.
- Scale-dependent: MAD is expressed in the same units as the data, making it difficult to compare across different datasets with different scales.
Despite its limitations, MAD remains a valuable tool for assessing forecast accuracy due to its simplicity and interpretability.
