🔬 MASE (Mean Absolute Scaled Error)

MASE (Mean Absolute Scaled Error)#

Forecast error scaled by a naive baseline’s error, comparable across series.

Important

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What it is#

Mean Absolute Scaled Error divides a forecast’s mean absolute error by the MAE of an in-sample naive benchmark — the seasonal-naive or last-value forecast — giving a pure ratio:

\[\text{MASE} = \frac{\text{MAE}_{\text{model}}}{\text{MAE}_{\text{naive}}}.\]

It answers a single question: did the model beat the trivial baseline?

Reading it#

MASE < 1 means the forecast outperforms naive; = 1 ties it; > 1 means the naive forecast wins and the model should be reconsidered. Because numerator and denominator share units, MASE is scale-free and comparable across series of wildly different magnitudes.

Why it’s the gold standard#

Unlike percentage errors, MASE is symmetric (over- and under-forecasts penalized equally), robust to zeros and outliers (the naive step is bounded away from zero unless the series is constant), and interpretable. Proposed by Hyndman & Koehler (2006), it is a default for forecasting competitions and multi-SKU demand.

Theme: Model Evaluation & Uncertainty · All terminology

Hint

Mind map — connected ideas

WMAPE (Weighted Mean Absolute Percentage Error) · sMAPE (Symmetric Mean Absolute Percentage Error) · Mean Absolute Percentage Error (MAPE) · Mean Absolute Error (MAE) · Root Mean Squared Error (RMSE) · Forecasting Competitions

Hint

More in Model Evaluation & Uncertainty

Average Absolute Error (AAE) · Baseline Heuristics · Bootstrap · Bootstrap Confidence Intervals (CIs) · Coverage · Cramér’s V · DeLong’s Test · KS Statistic (Kolmogorov–Smirnov Statistic) · Likelihood Ratio (LR) · Mann–Whitney U Test (also called the Wilcoxon rank-sum test) · Mean Absolute Error (MAE) · Mean Absolute Percentage Error (MAPE) · Mean Squared Error (MSE) · Relative accuracy