Data and calculation settings
Paste comma, tab, or semicolon separated data. A header row is recommended.
Formula used
ŷ ± z(1 − α/2) × SEŷ ± t(df, 1 − α/2) × SE[ŷ + Qα/2(residuals), ŷ + Q1−α/2(residuals)][ŷ − Q(1−α)(|residual|), ŷ + Q(1−α)(|residual|)]PICP = covered observations ÷ observations with actual valuesHow to use
Paste forecast data with clear column headers. Match each column name in the controls. Then choose the interval method.
Select a confidence level and uncertainty source. Adjust plot and filter settings as needed. Press the calculation button.
Review coverage, width, error, and diagnostic scores. Inspect missed observations in the table. Export results for further reporting.
Example data format
| Date | Actual | Forecast | StdError | Series |
|---|---|---|---|---|
| 2026-01 | 118 | 116 | 5.0 | Sales |
| 2026-02 | 124 | 122 | 5.5 | Sales |
| 2026-03 | 130 | 129 | 5.2 | Sales |
Method guidance
Normal bands suit approximately symmetric forecast errors. Student-t bands add protection for smaller samples. Empirical bands avoid a strict normality assumption.
Bootstrap bands simulate residual uncertainty using repeated samples. Conformal bands target distribution-free marginal coverage. Custom bounds preserve intervals produced elsewhere.
Pointwise bands cover each forecast separately. Simultaneous bands protect the full plotted family. Wider bands usually increase observed coverage.
Frequently asked questions
What is a forecast confidence band?
A band displays uncertainty around forecast values. It contains lower and upper limits. Wider bands represent greater uncertainty.
What confidence level should I choose?
Ninety-five percent is a common starting point. Higher levels produce wider intervals. Choose a level matching decision risk.
What is the difference between confidence and prediction intervals?
A mean interval estimates the expected response. A prediction interval covers future observations. Prediction intervals are normally wider.
When should I use empirical residual quantiles?
Use them when residuals look asymmetric or heavy-tailed. They preserve observed error shape. Enough residual observations are still required.
What does empirical coverage mean?
Coverage is the share of actual values inside intervals. Compare it with the selected confidence level. Large gaps indicate miscalibration.
What is interval sharpness?
Sharpness describes how narrow useful intervals are. Narrower intervals are more informative. Coverage must remain acceptably high.
Why are my bands extremely wide?
Residual variation may be large. Standard errors may also be overstated. Inspect outliers and changing variance.
Can I compare multiple forecast series?
Yes, include a series column. Diagnostics are calculated for each group. The chart displays separate forecast layers.
Can the calculator generate forecasts?
Yes, several baseline methods are included. They support quick uncertainty exploration. Dedicated modeling software may provide richer forecasts.