1. Definition
- The Average Absolute Error (AAE) is the mean of the absolute differences between actual values and predicted values.
- It measures the average size of forecast errors, without considering direction (over- or under-prediction).
$AAE = \frac{1}{n} \sum_{t=1}^n | y_t – \hat{y}_t |$
Where:
- $y_t$ = actual value at time $t$
- $\hat{y}_t$ = predicted (forecasted) value
- $n$ = number of forecasts
Note: AAE is essentially the same as Mean Absolute Error (MAE).
2. Interpretation
- AAE = 0 → perfect forecast.
- Larger AAE → on average, predictions are further away from actuals.
- Intuitive: “On average, how wrong is the model?”
3. Example
Suppose actual vs forecasted sales:
| Time | Actual ($y_t$) | Forecast ($\hat{y}_t$) | Error | Absolute Error |
|---|---|---|---|---|
| 1 | 100 | 90 | -10 | 10 |
| 2 | 120 | 115 | -5 | 5 |
| 3 | 130 | 140 | +10 | 10 |
$AAE = \frac{10 + 5 + 10}{3} = \frac{25}{3} \approx 8.33$
On average, the forecast is 8.3 units off.
4. Advantages
- Easy to interpret in the same units as the data.
- Less sensitive to extreme errors than squared-error metrics (like RMSE).
5. Limitations
- Doesn’t penalize large errors as heavily as RMSE.
- Not scale-independent → can’t directly compare across datasets with different scales (use MASE or MAPE instead).
6. Use Cases
- Forecast accuracy measurement in business (sales, demand, inventory).
- Regression model evaluation.
- Benchmarking models in competitions.
Summary:
Average Absolute Error (AAE) = the mean of absolute forecast errors. It’s the same as MAE, simple to compute, and easy to interpret: “on average, the forecast is off by X units.”