Forecast Performance Summary
Interpretation
Model Comparison
Forecast Horizon Analysis
Detailed Error Table
Charts
Formula Used
Error: eₜ = Actualₜ − Forecastₜ MAE = Σ|eₜ| / n MSE = Σeₜ² / n RMSE = √MSE MAPE = (100 / n) × Σ|eₜ / Actualₜ| sMAPE = (100 / n) × Σ[2|eₜ| / (|Actualₜ| + |Forecastₜ|)] WAPE = 100 × Σ|eₜ| / Σ|Actualₜ| MASE = MAE / MAE of the selected naïve benchmark Tracking Signal = Cumulative Forecast Error / MAD
Forecast error measures the difference between observed and predicted values. Smaller absolute metrics usually indicate better point forecasts. Bias metrics reveal systematic overforecasting or underforecasting.
How to Use
- Enter actual values and at least one forecast series.
- Add periods, weights, horizons, training data, or intervals when available.
- Select percentage-error, missing-data, weighting, and outlier settings.
- Choose the MASE benchmark and evaluation window.
- Click Calculate Forecast Error and review metrics, tables, charts, and interpretations.
- Copy, print, save, share, or export the completed analysis.
Example Data
| Month | Actual | Model A | Model B | Lower | Upper |
|---|---|---|---|---|---|
| Jan | 120 | 118 | 123 | 110 | 130 |
| Feb | 132 | 135 | 130 | 122 | 144 |
| Mar | 128 | 130 | 126 | 118 | 140 |
| Apr | 145 | 141 | 147 | 132 | 154 |
| May | 150 | 154 | 151 | 140 | 162 |
Frequently Asked Questions
What is forecast error?
Forecast error is the difference between an observed value and its prediction. The chosen sign convention determines its direction.
Which metric should I use?
MAE is easy to interpret, while RMSE penalises large misses. MASE is useful for comparisons across different scales.
Why can MAPE be misleading?
MAPE is undefined when actual values equal zero. It can also exaggerate errors when actual values are very small.
What does positive bias mean?
With Actual minus Forecast, positive bias indicates underforecasting. Negative bias indicates predictions are systematically too high.
Why is RMSE larger than MAE?
RMSE squares errors before averaging them. Large errors therefore receive much greater influence than small errors.
What is a good MASE value?
A MASE below one beats the selected naïve benchmark. Values above one indicate weaker average absolute performance.
What does tracking signal show?
Tracking signal compares cumulative bias with average absolute deviation. Large magnitudes can indicate persistent forecast bias.
Can I compare several models?
Yes. Enter Model B and Model C to rank forecasts using your selected accuracy metric.
How are prediction intervals evaluated?
The calculator reports coverage, average width, violations, and interval scores. Good intervals balance coverage with narrow widths.