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	ETS: Wykładnicze wygładzanie z uwzględnieniem błędu, trendu i sezonowości	Prophet	SARIMAX
Dziedzina	Ekonometria	Ekonometria	Ekonometria
Rodzina	Regression model	Regression model	Regression model
Rok powstania	2008	2018	2015
Twórca	Hyndman, Koehler, Ord & Snyder (state space framework)	Taylor & Letham (Facebook/Meta)	Box & Jenkins (ARIMA framework); SARIMAX extension with exogenous regressors
Typ	Exponential smoothing state space model	Decomposable (structural) time series model	Seasonal time-series regression model
Źródło pierwotne	Hyndman, R. J., Koehler, A. B., Ord, J. K. & Snyder, R. D. (2008). Forecasting with Exponential Smoothing: The State Space Approach. Springer.	Taylor, S. J. & Letham, B. (2018). Forecasting at Scale. The American Statistician, 72(1), 37-45.	Hyndman, R. J. & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.
Inne nazwy	exponential smoothing state space model, innovations state space model, Holt-Winters family, ETS — Hata/Trend/Mevsimsellik Üstel Düzleştirme	Prophet, Facebook Prophet, Meta Prophet, forecasting at scale	seasonal ARIMA with exogenous variables, SARIMA with regressors, ARIMAX, SARIMAX — Dışsal Değişkenli Mevsimsel ARIMA
Pokrewne	5	5	4
Podsumowanie	ETS is a comprehensive exponential smoothing framework that automatically selects additive or multiplicative combinations of the error (E), trend (T) and seasonal (S) components of a time series. Formalised as an innovations state space model by Hyndman, Koehler, Ord and Snyder in 2008, it unifies and generalises the Holt-Winters family of forecasting methods.	Prophet is a Bayesian structural time series model introduced by Taylor and Letham at Facebook/Meta in 2018. It forecasts a continuous series by decomposing it into separate, interpretable trend, seasonality, and holiday components, and is designed to be approachable for analysts working at scale.	SARIMAX extends the seasonal ARIMA (Box-Jenkins) model by adding exogenous explanatory variables, so it can capture the effect of holidays, economic indicators, or policy variables on a time series. It combines non-seasonal and seasonal autoregressive and moving-average dynamics with external regressors, and is estimated by maximum likelihood in state-space form.