Both SARIMA and Prophet extend a history of observed values (the pale ribbon) into the future, but they lean on different mechanics. SARIMA (orange) is a seasonal extension of ARIMA: it differences the series and fits autoregressive and moving-average terms on the seasonal cycle, so it reproduces the shape of past seasons well but has no built-in concept of a one-off calendar event. Prophet (blue) is an additive model — trend + yearly seasonality + explicit holiday regressors — built for business series with irregular spikes.
Prophet was released by Facebook's Core Data Science team in 2017 specifically because analysts kept fighting classical ARIMA to bolt on holidays, promotions and multiple seasonal cycles — problems Prophet handles as first-class model inputs instead of afterthoughts.
A synthetic monthly time series with trend, seasonality and an optional December spike is extended into the future by two forecast ribbons — SARIMA in orange, Prophet in blue — so you can see exactly where their mechanics diverge.
Both models extrapolate the same learned trend and seasonal cycle, but SARIMA has no holiday term and smooths straight through the December spike, while Prophet's explicit holiday regressor reproduces it. Their uncertainty bands also widen at different rates.
Adjust seasonal amplitude, trend slope and noise to reshape the observed history, set the forecast horizon, and toggle the holiday effect to watch the two forecast ribbons agree or disagree. Resample noise for a fresh random history.
Facebook's Core Data Science team built Prophet in 2017 because analysts kept hand-engineering holiday dummies into ARIMA models — Prophet turns that workaround into a first-class, tunable model component.