Prophet Forecast Tool Calculator

Inputs

Example Data Table

Use this structure in your CSV or pasted lines.

Formula Used

This calculator uses a decomposable forecasting model:

• Linear mode: ŷ(t) = g(t) + s(t) + h(t)
• Logistic mode: z(t) = logit((y(t)−floor)/(cap−floor)), then ẑ(t) = g(t)+s(t)+h(t), and ŷ(t)=inverse-logit(ẑ(t))

Trend g(t) is a piecewise linear function with changepoints:

g(t) = β0 + β1·t + Σj δj·max(0, t − cj)

Seasonality s(t) uses Fourier series terms for enabled periods:

s(t) = Σk [ ak·sin(2πk·t/P) + bk·cos(2πk·t/P) ]

Holiday effects h(t) use an indicator regressor:

h(t) = γ·I(t is a holiday)

Parameters are fitted with ridge-regularized least squares: β = (XᵀX + λI)⁻¹ Xᵀy where λ is derived from the prior-strength inputs to stabilize estimates.

How to Use This Calculator

1. Paste your time series as date,value lines or upload a CSV.
2. Select frequency, horizon, and growth type. Use logistic only when you know realistic cap and floor.
3. Enable seasonalities and choose Fourier terms (K). Start small, then increase if needed.
4. Enable changepoints for series with shifts. More changepoints can overfit noisy data.
5. Optionally add holidays as dates to capture spikes or dips.
6. Run the forecast. Review intervals, then export CSV or PDF for reporting.

Decomposable structure for practical forecasting

This tool models a time series as trend, seasonality, and optional holiday effects, producing forecasts that remain interpretable under business scrutiny. The trend component captures baseline growth and allows shifts through changepoints, which are spaced across the observed history. Seasonal components use Fourier terms to represent repeating patterns without requiring dummy variables for every calendar position. Holiday indicators add a targeted lift or drop on specified dates, helping explain promotional spikes and operational slowdowns.

Trend flexibility with changepoints

Piecewise linear trend improves fit when the underlying level changes because of pricing, policy, channel mix, or supply constraints. Each changepoint introduces a hinge feature max(0, t − c), allowing slope adjustments after c. More changepoints increase flexibility but can chase noise, so the prior-strength input stabilizes estimates via ridge regularization. Begin with moderate changepoints, review residual variability, then simplify if intervals widen too much.

Seasonality design and Fourier terms

Weekly, monthly, and yearly seasonalities are optional because not every series repeats on all cycles. Each enabled seasonality adds 2K sine and cosine terms, where K controls smoothness versus responsiveness. Small K values capture broad oscillations; larger K values represent sharper peaks, such as weekend surges. When sampling is weekly or monthly, periods are still represented on the internal day-based index, keeping the feature design consistent.

Uncertainty intervals for decision support

The forecast includes lower and upper bounds computed from residual dispersion and a selected confidence level. Residual standard deviation summarizes how well the fitted structure explains history. Wider intervals may indicate regime changes, missing regressors, or irregular data. Narrow intervals suggest stable patterns but should still be stress-tested with different seasonality settings. Exportable outputs support scenario review, reporting, and downstream planning.

Data handling and export workflow

Inputs accept pasted lines or a CSV file containing date and value columns, with automatic sorting and de-duplication by date. Frequency detection uses median spacing and guides future date stepping. Logistic growth can be chosen when realistic floor and cap bounds exist, preventing runaway forecasts. After running the model, results appear above the form for iteration, and exports provide a CSV or a compact PDF summary.

FAQs

What data frequency works best?

Use consistent spacing between dates. The tool can detect daily, weekly, or monthly spacing, but mixed intervals reduce accuracy. If your data is irregular, resample or aggregate first to stabilize trend and seasonal signals.

How many changepoints should I use?

Start with 6 to 10 for medium histories. Increase if you know there were multiple structural shifts. Decrease when forecasts look overly reactive or intervals become very wide.

When should I choose logistic growth?

Choose logistic when your metric has a natural ceiling and floor, such as capacity, saturation, or bounded rates. Set cap and floor realistically; otherwise the transformation can distort the fit.

How do Fourier terms affect results?

Fourier terms control seasonal detail. Lower K yields smoother waves, while higher K captures sharper peaks. Raise K gradually and stop when validation or interval stability stops improving.

What do the confidence bounds represent?

Bounds are built from residual variability and your chosen confidence level. They approximate uncertainty around the forecast, not guaranteed limits. Large bounds signal noise, missing drivers, or changing behavior.

Can I include special events and holidays?

Yes. Enable holidays and list dates, optionally with names. The model adds an indicator feature for those dates so the forecast can account for repeatable event effects.