مقایسهٔ روش‌ها

	ETS: هموارسازی نمایی خطا، روند، فصلی	هموارسازی نمایی سه‌گانه هولت-وینترز	SARIMAX
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	2008	1960	2015
پدیدآور	Hyndman, Koehler, Ord & Snyder (state space framework)	Charles C. Holt and Peter R. Winters	Box & Jenkins (ARIMA framework); SARIMAX extension with exogenous regressors
نوع	Exponential smoothing state space model	Exponential smoothing forecasting model	Seasonal time-series regression model
منبع بنیادین	Hyndman, R. J., Koehler, A. B., Ord, J. K. & Snyder, R. D. (2008). Forecasting with Exponential Smoothing: The State Space Approach. Springer.	Winters, P. R. (1960). Forecasting Sales by Exponentially Weighted Moving Averages. Management Science, 6(3), 324-342.	Hyndman, R. J. & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.
نام‌های دیگر	exponential smoothing state space model, innovations state space model, Holt-Winters family, ETS — Hata/Trend/Mevsimsellik Üstel Düzleştirme	triple exponential smoothing, Winters' method, Holt-Winters seasonal method, Holt-Winters Üçlü Üstel Düzleştirme	seasonal ARIMA with exogenous variables, SARIMA with regressors, ARIMAX, SARIMAX — Dışsal Değişkenli Mevsimsel ARIMA
مرتبط	5	4	4
خلاصه	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.	Holt-Winters triple exponential smoothing is a forecasting model that extends Holt's double smoothing by adding a seasonal component, introduced by Peter Winters in 1960 building on Charles Holt's work. It tracks three evolving quantities — level, trend, and season — and combines them to forecast a continuous time series.	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.