قارن الطرق

	ETS: تنعيم أسي للخطأ والاتجاه والموسمية	Prophet	SARIMAX
المجال	الاقتصاد القياسي	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model	Regression model
سنة النشأة	2008	2018	2015
صاحب الطريقة	Hyndman, Koehler, Ord & Snyder (state space framework)	Taylor & Letham (Facebook/Meta)	Box & Jenkins (ARIMA framework); SARIMAX extension with exogenous regressors
النوع	Exponential smoothing state space model	Decomposable (structural) time series model	Seasonal time-series regression model
المصدر التأسيسي	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.
الأسماء البديلة	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
ذات صلة	5	5	4
الملخص	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.