Average Absolute Error (AAE)

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).

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2. Interpretation

• AAE = 0 → perfect forecast.
• Larger AAE → on average, predictions are further away from actuals.
• Intuitive: “On average, how wrong is the model?”

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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.

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4. Advantages

• Easy to interpret in the same units as the data.
• Less sensitive to extreme errors than squared-error metrics (like RMSE).

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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).

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6. Use Cases

• Forecast accuracy measurement in business (sales, demand, inventory).
• Regression model evaluation.
• Benchmarking models in competitions.

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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.”