Mean Absolute Scaled Error (MASE)
Also known as: MASE
Mean Absolute Scaled Error is a scale-independent metric that measures prediction accuracy relative to a simple baseline (naive forecast). Introduced by Hyndman and Koehler (2006), MASE directly compares model performance to a reference method, overcoming limitations of MAPE and other percentage-based metrics.
Key highlights
- Scale-independent: directly comparable across datasets
- Handles zero values gracefully; no division by actual or predicted values
- Intuitive interpretation: MASE < 1 means better than naive baseline
- Robust to outliers (uses MAE denominator, not squared errors)
Intuition
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How it works
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When to use it
Use MASE when comparing models across different datasets or scales, or when your data contains zeros or very small values. MASE is ideal for forecasting tasks where a naive baseline is meaningful (e.g., time-series). It directly answers the question: Is my model better than simple past-value prediction? The metric works with any data scale and is robust to outliers.
Strengths & limitations
- Scale-independent: directly comparable across datasets
- Handles zero values gracefully; no division by actual or predicted values
- Intuitive interpretation: MASE < 1 means better than naive baseline
- Robust to outliers (uses MAE denominator, not squared errors)
- Only meaningful for time-series data where naive baseline is applicable
- For non-sequential or cross-sectional data, the baseline may not be meaningful
- Denominator can be very small if naive baseline has low error, causing instability
- Requires test set; not a direct metric of absolute accuracy
Common pitfalls
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Applications
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Frequently asked
What is the naive baseline in MASE?
The naive forecast is the simplest possible prediction: assume the next value equals the previous value (one-step-ahead naive forecast). For seasonal data, some use the seasonal naive baseline (previous value from the same season).
Can I use MASE with non-time-series data?
Technically yes, but the naive baseline becomes arbitrary without a natural ordering. For cross-sectional data, consider other metrics like MAE, RMSE, or relative metrics that compare to a domain-relevant baseline.
What if the naive baseline has zero error?
This is rare but problematic. If the naive forecast is perfect, MASE is undefined. In practice, if naive error is very small, MASE becomes unstable. Use alternative metrics if this occurs.
Is MASE the best metric for all forecasting problems?
Not universally. MASE is excellent for comparing models and handling zeros, but it does not directly reflect accuracy in original units (like MAE or RMSE) or percentage terms (like MAPE). Use multiple metrics for complete insight.
How does MASE perform with trend or seasonality?
MASE with a simple naive baseline can be misleading for data with strong trends or seasonality. Consider using a seasonal naive baseline instead, or use a more sophisticated baseline that accounts for these patterns.
Sources
- 1.Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679-688.
- 2.Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). Melbourne, Australia: OTexts.
- 3.Wang, X., & Petropoulos, F. (2016). To select or to combine? Forecasting from a thousand models. International Journal of Forecasting, 32(3), 594-606.
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Cite this page
ScholarGate. (2026, June 3). Mean Absolute Scaled Error. ScholarGate. https://scholargate.app/model-evaluation/mean-absolute-scaled-error