What is mean absolute error (MAE) in time series forecasting?

What is Mean Absolute Error (MAE) in Time Series Forecasting? Mean Absolute Error (MAE) is a metric used to measure the average magnitude of errors between predicted and actual values in time series forecasting. It calculates the absolute difference between each forecasted value and the corresponding observed value, then averages these differences. Unlike metrics that square errors (e.g., Mean Squared Error), MAE treats all errors equally, making it intuitive and resistant to outliers. For example, if a model predicts daily sales, MAE tells you how far off the predictions are, on average, from the true sales numbers.

Calculation and Interpretation To compute MAE, take the absolute value of each prediction error (predicted minus actual value), sum these absolute errors, and divide by the number of observations. Mathematically, MAE = (1/n) * Σ|Actualₜ - Predictedₜ|, where n is the number of data points. Suppose you forecast temperatures for three days: actuals are [15°C, 20°C, 25°C], and predictions are [16°C, 18°C, 23°C]. The absolute errors are [1, 2, 2], so MAE = (1+2+2)/3 ≈ 1.67°C. This means, on average, predictions are off by ~1.67°C. MAE’s simplicity makes it easy to explain—for instance, a retail developer might use it to quantify a model’s average error in predicting weekly inventory demand.

When to Use MAE and Considerations MAE is ideal when you want a straightforward measure of average error magnitude without emphasizing large errors disproportionately. For example, in energy load forecasting, if a utility company cares equally about small and large prediction errors, MAE provides a clear performance snapshot. However, MAE doesn’t indicate error direction (over- or under-prediction) or penalize large deviations heavily, which might be critical in scenarios like flood prediction. Developers often pair MAE with other metrics (e.g., RMSE) for a fuller picture. When optimizing models, minimizing MAE aligns with reducing average error, but it may require robust optimization techniques since the absolute value function isn’t differentiable at zero. In practice, libraries like Python’s scikit-learn provide built-in MAE functions, enabling developers to compute it efficiently during model evaluation.