Mean Absolute Scaled Error Calculator
Scales forecast absolute error by the in-sample naive forecast error. The form displays MAE forecast / in-sample naive MAE beside mean absolute scaled error, using a worked condition that can be recalculated with the labeled inputs.
Describe the observed sequence in this example
Mean absolute scaled error
The question behind mean absolute scaled error
The mean absolute scaled error page scales forecast absolute error by the in-sample naive forecast error.
Mean absolute scaled error is limited to the statistical quantity named by the result panel. The mean absolute scaled error calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Inputs that define mean absolute scaled error
- Actual values: For mean absolute scaled error, the displayed actual values sequence is 12, 15, 18, 21, 24, 27. Preserve actual values order when mean absolute scaled error depends on pairing, lag, rank, or time position, and distinguish an observed zero from a missing actual values entry.
- Forecast values: For mean absolute scaled error, the displayed forecast values sequence is 13, 14, 19, 20, 25, 26. Preserve forecast values order when mean absolute scaled error depends on pairing, lag, rank, or time position, and distinguish an observed zero from a missing forecast values entry.
- Seasonal period: For mean absolute scaled error, the worked value for seasonal period is 1 periods. Treat the seasonal period entry (1 periods) explicitly as a count, proportion, rate, estimate, or model parameter before comparing mean absolute scaled error conditions. The form enforces minimum 1.
The entries used for mean absolute scaled error must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid mean absolute scaled error arithmetic for a nonexistent study.
Working through the mean absolute scaled error formula
For mean absolute scaled error, match every symbol in the relationship to a labeled field before substituting numbers. Mean absolute scaled error is reported in ratio.
While checking mean absolute scaled error, use actual values observations from one defined analysis set rather than totals copied from incompatible groups.
For a related comparison, continue with autocovariance and mean absolute percentage error.
A reproducible mean absolute scaled error case
The default mean absolute scaled error condition is Actual values = 12, 15, 18, 21, 24, 27, Forecast values = 13, 14, 19, 20, 25, 26, Seasonal period = 1 periods.
The example produces a MASE of about 0.3333.
The live calculator reports MASE 0.33333333 · Forecast MAE 1. Repeating one intermediate step from MAE forecast / in-sample naive MAE provides a fixed mean absolute scaled error reference check for later code changes.
Assumptions behind mean absolute scaled error
A MASE below one indicates improvement over the chosen naive benchmark, provided the benchmark denominator is nonzero and comparable.
For mean absolute scaled error, time order is part of the data. For mean absolute scaled error, reordering observations, changing the forecast origin, or mixing incomplete seasonal cycles changes the statistical question.
A second check on mean absolute scaled error
When interpreting mean absolute scaled error, keep the lag, window, seasonal period, initialization rule, and forecast horizon with the result so a later calculation uses the same timeline.
As a second check for mean absolute scaled error, outliers, ties, ordering, and missing entries can affect mean absolute scaled error even when the number of observations stays unchanged.
A practical stress test for mean absolute scaled error
Change actual values while holding the remaining entries fixed, then state why the direction and size of the mean absolute scaled error change are plausible from MAE forecast / in-sample naive MAE.
Repeat the mean absolute scaled error exercise with seasonal period. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that mean absolute scaled error scenario as exact.
Where a plausible mean absolute scaled error can go wrong
Before accepting mean absolute scaled error, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For mean absolute scaled error, do not substitute zero for an unobserved value; missingness and a measured zero describe different data.
Another mean absolute scaled error failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on mean absolute scaled error, then round only the reported value.
Rebuilding this mean absolute scaled error calculation later
Report mean absolute scaled error using MAE forecast / in-sample naive MAE, followed by the entered values, units, exclusions, and analysis date. Name the mean absolute scaled error population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including MASE 0.33333333 · Forecast MAE 1. A later mean absolute scaled error review can then distinguish a changed input from a different convention or software implementation.
Questions about mean absolute scaled error
How should mean absolute scaled error be rounded?
Keep the unrounded mean absolute scaled error for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in mean absolute scaled error do not correct sampling or model error.
Which input deserves the closest boundary check?
For mean absolute scaled error, start with seasonal period and then actual values. Confirm the mean absolute scaled error units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.
Why could another program report a different mean absolute scaled error?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change mean absolute scaled error. Compare the printed mean absolute scaled error formula and its input definitions before treating either output as wrong.