Predictive Analytics: Time-Series Forecast Simulator

Forecast Model

Trend strength 0.04

Seasonality amplitude 1.0

Noise level 0.5

Forecast horizon 18 steps

Steps revealed

0 / 0

95% CI coverage

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Forecast RMSE

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Band width @ horizon

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How it works

The historical series is generated from a trend plus a repeating seasonal cycle plus random noise — the same additive structure classical models like ARIMA and Prophet fit to real data. The forecast model has learned the true trend and seasonal pattern, so its projection (teal line) is exact — but it cannot know the future noise, so its confidence interval must widen the further out it forecasts, since each extra step adds another independent chance for noise to push the real value away from the line.

y(t)    = trend·t + amp·sin(2π·t / period) + noise·ε
ŷ(t)    = trend·t + amp·sin(2π·t / period)          (model's best estimate)
CI(t)   = ± 1.96 · noise · √(t − t_now)              (95% interval, grows with horizon)

Trend strength — the steady upward or downward slope baked into the data, like long-run demand growth.
Seasonality amplitude — how strongly the repeating cycle (e.g. weekly or seasonal demand swings) affects the series.
Noise level — random, unpredictable variation; higher noise both roughens the historical data and widens the forecast's confidence band.
Forecast horizon — how many steps ahead the model projects. Watch the playback cursor cross into the forecast zone and see how many of the real future points (orange) stay inside the confidence ribbon versus how many the model missed.

Real-world relevance: this trend + seasonality + noise decomposition, and the widening uncertainty band, is exactly what a demand-forecasting or capacity-planning dashboard shows — a forecast is only as trustworthy as its confidence interval.

Historical data Forecast (ŷ) Actual future point Playback cursor

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