So sánh phương pháp

	SARIMA (Seasonal ARIMA)	ETS: Error, Trend, Seasonal Exponential Smoothing	Prophet	SARIMAX
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model	Regression model	Regression model
Năm ra đời	2015	2008	2018	2015
Người khởi xướng	Box & Jenkins (seasonal extension of ARIMA)	Hyndman, Koehler, Ord & Snyder (state space framework)	Taylor & Letham (Facebook/Meta)	Box & Jenkins (ARIMA framework); SARIMAX extension with exogenous regressors
Loại	Seasonal time-series model	Exponential smoothing state space model	Decomposable (structural) time series model	Seasonal time-series regression model
Công trình gốc	Box, G.E.P., Jenkins, G.M., Reinsel, G.C. & Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021	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.
Tên gọi khác	seasonal ARIMA, Box-Jenkins seasonal model, SARIMA — Mevsimsel ARIMA	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
Liên quan	5	5	5	4
Tóm tắt	SARIMA is a seasonal extension of the Box-Jenkins ARIMA model that adds seasonal differencing and seasonal autoregressive and moving-average terms. Developed within the Box, Jenkins, Reinsel and Ljung framework (5th edition, 2015), it forecasts series whose pattern repeats on a yearly, monthly, or weekly period.	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.