Calculator Inputs
Enter a numeric time series, choose an interval setup, and calculate future uncertainty bands. Results appear above this form after submission.
Example Data Table
| Period | Observed Value | Forecast | Lower Bound | Upper Bound |
|---|---|---|---|---|
| T1 | 120 | — | — | — |
| T2 | 124 | — | — | — |
| T3 | 127 | — | — | — |
| T4 | 131 | — | — | — |
| T5 | 136 | — | — | — |
| T6 | 140 | — | — | — |
| T7 | 145 | — | — | — |
| T8 | 149 | — | — | — |
| T9 | — | 153.25 | 146.60 | 159.90 |
| T10 | — | 156.00 | 147.90 | 164.10 |
| T11 | — | 158.75 | 149.05 | 168.45 |
Formula Used
Residual error: σ = √[Σ(et − ē)² / (m − 1)]
Critical value: c comes from the selected Z or t distribution at the chosen confidence level.
Prediction interval: ŷh ± c × σ × gh
Confidence interval: ŷh ± c × (σ / √n) × gh
Growth factor: gh = 1 for constant width, or √h for widening uncertainty over longer horizons.
Here, ŷh is the forecast for future period h, σ is the residual standard error, n is the number of observations, and m is the number of residuals.
How to Use This Calculator
- Paste your historical values into the series box using commas, spaces, or new lines.
- Choose a forecast method such as last value, mean, moving average, or drift.
- Set the forecast horizon and confidence level for the interval estimate.
- Pick prediction or confidence interval depending on whether you want future-value uncertainty or estimate uncertainty.
- Select constant or √h growth if you expect interval width to remain steady or expand over time.
- Use custom forecast values when you already have baseline future estimates from another model.
- Press Calculate Interval to show the result summary, chart, and future interval table above the form.
- Use the CSV and PDF buttons to export the current results for reporting or review.
FAQs
1. What does this calculator estimate?
It estimates future time series intervals around forecast values. You can generate prediction intervals for future observations or confidence intervals for forecast estimates.
2. What is the difference between prediction and confidence intervals?
Prediction intervals are wider because they cover uncertainty in future values. Confidence intervals are narrower because they focus on uncertainty around the estimated forecast mean.
3. Why do intervals widen as the horizon increases?
Longer forecast horizons often carry more uncertainty. The √h option increases the standard error gradually, which creates wider intervals farther into the future.
4. When should I use custom forecast values?
Use custom forecasts when another model already produced future baseline values. This calculator then wraps uncertainty intervals around those supplied forecasts.
5. Which distribution should I choose?
Auto is usually fine. It leans toward t values for smaller samples and Z values for larger samples. Manual selection is useful for specific analytical standards.
6. What does residual standard error mean?
Residual standard error summarizes the typical forecast miss from the selected method. Larger values create wider intervals because uncertainty is higher.
7. Can I use trending or seasonal data?
Yes, but choose a suitable forecast method. Drift helps with trend, while custom forecast values are better when seasonality was modeled elsewhere.
8. Why are my intervals very narrow or zero?
This usually happens when the series changes very little, the residual error is near zero, or you selected a confidence interval with a stable dataset.