Root Mean Squared Forecast Error Calculator
Calculates the square-root mean squared error of a forecast sequence. The form displays sqrt(mean((actual−forecast)^2)) beside root mean squared forecast error, using a worked condition that can be recalculated with the labeled inputs.
Enter the source values at the selected scale
Root mean squared forecast error
Interpreting the requested root mean squared forecast error
The root mean squared forecast error page calculates the square-root mean squared error of a forecast sequence.
Root mean squared forecast error is limited to the statistical quantity named by the result panel. The root mean squared forecast error calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
Measurements required for root mean squared forecast error
- Actual values: For root mean squared forecast error, the displayed actual values sequence is 12, 15, 18, 21, 24, 27. Preserve actual values order when root mean squared forecast error depends on pairing, lag, rank, or time position, and distinguish an observed zero from a missing actual values entry.
- Forecast values: For root mean squared forecast error, the displayed forecast values sequence is 13, 14, 19, 20, 25, 26. Preserve forecast values order when root mean squared forecast error depends on pairing, lag, rank, or time position, and distinguish an observed zero from a missing forecast values entry.
The entries used for root mean squared forecast error must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid root mean squared forecast error arithmetic for a nonexistent study.
From inputs to root mean squared forecast error
For root mean squared forecast error, match every symbol in the relationship to a labeled field before substituting numbers. Root mean squared forecast error is reported in units.
While checking root mean squared forecast error, use actual values observations from one defined analysis set rather than totals copied from incompatible groups.
A fixed case for comparison
The default root mean squared forecast error condition is Actual values = 12, 15, 18, 21, 24, 27, Forecast values = 13, 14, 19, 20, 25, 26.
The example RMSFE is 1.
The live calculator reports RMSFE 1. Repeating one intermediate step from sqrt(mean((actual−forecast)^2)) provides a fixed root mean squared forecast error reference check for later code changes.
Limits on interpreting root mean squared forecast error
RMSFE emphasizes larger misses and should be reported with the forecast horizon and evaluation window.
For root mean squared forecast error, time order is part of the data. For root mean squared forecast error, reordering observations, changing the forecast origin, or mixing incomplete seasonal cycles changes the statistical question.
Reading root mean squared forecast error in context
When interpreting root mean squared forecast 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 root mean squared forecast error, outliers, ties, ordering, and missing entries can affect root mean squared forecast error even when the number of observations stays unchanged.
For a related comparison, continue with symmetric mean absolute percentage error.
Testing how stable root mean squared forecast error is
Change actual values while holding the remaining entries fixed, then state why the direction and size of the root mean squared forecast error change are plausible from sqrt(mean((actual−forecast)^2)).
Repeat the root mean squared forecast error exercise with forecast values. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that root mean squared forecast error scenario as exact.
What to record with root mean squared forecast error
Report root mean squared forecast error using sqrt(mean((actual−forecast)^2)), followed by the entered values, units, exclusions, and analysis date. Name the root mean squared forecast error population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including RMSFE 1. A later root mean squared forecast error review can then distinguish a changed input from a different convention or software implementation.
Questions about root mean squared forecast error
Why could another program report a different root mean squared forecast error?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change root mean squared forecast error. Compare the printed root mean squared forecast error formula and its input definitions before treating either output as wrong.
What does root mean squared forecast error represent on this page?
It is the quantity produced by sqrt(mean((actual−forecast)^2)) from the displayed actual values, forecast values. This page calculates the square-root mean squared error of a forecast sequence.
What should be saved with root mean squared forecast error?
Save the entered values and units for actual values, forecast values, along with the analysis date, exclusions, software or formula version, and the relationship sqrt(mean((actual−forecast)^2)). That record is sufficient to rebuild this specific root mean squared forecast error calculation.
Does root mean squared forecast error establish a causal or population conclusion?
No. The displayed root mean squared forecast error value is conditional on the entered data and named method. The root mean squared forecast error design, measurement process, and assumptions determine what can be concluded beyond those values.
How should root mean squared forecast error be rounded?
Keep the unrounded root mean squared forecast error for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in root mean squared forecast error do not correct sampling or model error.
Which input deserves the closest boundary check?
For root mean squared forecast error, start with forecast values and then actual values. Confirm the root mean squared forecast error units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.