Mean Absolute Scaled Error Calculator

Calculation Results

Waiting for data

Enter training data, actual values, and one forecast model. Results will appear here after calculation.

Best MASE

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Forecast MAE

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Naïve Benchmark MAE

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Scaling Denominator

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Total Absolute Error

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Forecast Bias

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RMSE

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sMAPE

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WAPE

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Observations

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Training Length

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Seasonal Period

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Aggregate Model MASE

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Model Ranking

Rank	Model	MASE	MAE	RMSE	sMAPE	WAPE	Bias	Assessment

Observation Details

The table displays the best-ranked model. Large errors receive visual emphasis.

Period	Actual	Forecast	Error	Absolute Error	Per-Horizon MASE	Cumulative MASE	Rolling MASE

Calculation Summary

Calculation Mode

Mode

Decimal precision

Input delimiter

Time-Series Data

Import CSV

Training series

The naïve scaling denominator uses these historical values.

Actual test values

Enter observed values for the forecast horizon.

Observation weights

Weights must match the test observation count.

Data frequency

Seasonal period

Use 1 for non-seasonal data.

Missing-data handling

Calculate weighted MASE

Use epsilon protection

Epsilon value

Large-error threshold

Blank uses mean plus one standard deviation.

Rolling MASE window

Uses recent forecast errors within each window.

Percentage metrics

Optional period labels

Forecast Models

Formula Used

MASE = Mean(|Actual − Forecast|) ÷ Mean(|Trainingₜ − Trainingₜ₋ₘ|)

Weighted MASE = Weighted Mean Absolute Error ÷ Scaling Denominator

Here, m is the selected seasonal period. A value of one creates a non-seasonal naïve benchmark. The denominator should normally use only training observations.

How to Use

Enter historical training observations in chronological order.
Enter actual test values for the forecast horizon.
Add one or more model forecast series.
Select the correct seasonal period for your data.
Choose missing-data and weighting options when required.
Press Calculate MASE and review every comparison.

Example Data

Series	Values	Purpose
Training	120, 128, 133, 140, 147, 155, 162, 170	Builds the naïve scale.
Actual	176, 181, 189, 194	Provides observed test values.
Model A	174, 184, 187, 196	Tests a stronger forecast.
Model B	169, 177, 183, 188	Tests a weaker forecast.

Interpretation Guide

MASE Result	Meaning
Below 1	The model beats the naïve benchmark.
Equal to 1	The model matches the naïve benchmark.
Above 1	The model performs worse than the benchmark.
Equal to 0	The forecast perfectly matches every actual value.
Undefined	The scaling denominator is zero without protection.

Frequently Asked Questions

What does MASE measure?

MASE compares model error with naïve forecast error. It remains unit-free across different datasets. Lower values usually indicate stronger forecasting performance.

Why use training data for scaling?

Training data creates an independent benchmark scale. It avoids using information from evaluated forecasts. This supports fair comparisons between different models.

Which seasonal period should I choose?

Choose a period matching the repeating cycle. Monthly data often uses twelve observations. Non-seasonal series normally use a period of one.

Can MASE be negative?

Standard MASE cannot be negative. Both numerator and denominator use absolute differences. Invalid negative inputs indicate another processing problem.

What causes undefined MASE?

A constant training series creates zero naïve error. Division by zero then becomes impossible. Epsilon protection can provide an adjusted result.

Is MASE a percentage?

MASE is a dimensionless error ratio. It should not receive a percentage symbol. Percentage metrics remain separately available for comparison.

Can I compare multiple models?

Yes, add several forecast model series. The calculator ranks every valid model automatically. The lowest defined MASE receives first place.

What does weighted MASE change?

Weights increase selected observations' influence. Larger weights matter more during MAE calculation. The benchmark denominator remains based on training data.

How are missing values handled?

You can reject, remove, or replace them. Forward filling and interpolation are also supported. The chosen method appears within the summary.