So sánh phương pháp

	SARIMAX	Làm mịn mũ ba theo phương pháp Holt-Winters	Mô hình không gian trạng thái (Bộ lọc Kalman)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model	Regression model
Năm ra đời	2015	1960	1990
Người khởi xướng	Box & Jenkins (ARIMA framework); SARIMAX extension with exogenous regressors	Charles C. Holt and Peter R. Winters	Harvey; Durbin & Koopman (state space treatment); Kalman filter
Loại	Seasonal time-series regression model	Exponential smoothing forecasting model	State space time series model
Công trình gốc	Hyndman, R. J. & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.	Winters, P. R. (1960). Forecasting Sales by Exponentially Weighted Moving Averages. Management Science, 6(3), 324-342.	Harvey, A. C. (1990). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.
Tên gọi khác	seasonal ARIMA with exogenous variables, SARIMA with regressors, ARIMAX, SARIMAX — Dışsal Değişkenli Mevsimsel ARIMA	triple exponential smoothing, Winters' method, Holt-Winters seasonal method, Holt-Winters Üçlü Üstel Düzleştirme	state space, Kalman filter, unobserved components model, Durum Uzayı Modeli (State Space / Kalman Filter)
Liên quan	4	4	4
Tóm tắt	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.	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.	A state space model is a general time series framework that describes a series through unobserved (latent) state variables linked by a measurement equation and a transition equation, with the states estimated in real time by the Kalman filter. Developed in the state space tradition of Harvey (1990) and Durbin & Koopman (2012), it nests ARIMA and exponential smoothing as special cases.