Linganisha mbinu

	SARIMAX	Uchanganuzi wa Regresheni wa Kiotomatiki wa Bayesian (BVAR)	Ulainishaji Lainifu wa Kielelezo Mara Tatu wa Holt-Winters	Mfumo wa Nafasi ya Hali (Kichujio cha Kalman)
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model	Regression model
Mwaka wa asili	2015	1986	1960	1990
Mwanzilishi	Box & Jenkins (ARIMA framework); SARIMAX extension with exogenous regressors	Litterman (1986); Bańbura, Giannone & Reichlin (2010)	Charles C. Holt and Peter R. Winters	Harvey; Durbin & Koopman (state space treatment); Kalman filter
Aina	Seasonal time-series regression model	Bayesian multivariate time-series model	Exponential smoothing forecasting model	State space time series model
Chanzo asilia	Hyndman, R. J. & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.	Litterman, R. B. (1986). Forecasting with Bayesian Vector Autoregressions—Five Years of Experience. Journal of Business & Economic Statistics, 4(1), 25-38.	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.
Majina mbadala	seasonal ARIMA with exogenous variables, SARIMA with regressors, ARIMAX, SARIMAX — Dışsal Değişkenli Mevsimsel ARIMA	BVAR, Bayesian vector autoregression, Minnesota prior VAR, Bayesian VAR (BVAR)	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)
Zinazohusiana	4	5	4	4
Muhtasari	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.	Bayesian VAR adds Minnesota or other prior distributions to a vector autoregressive model to control over-parameterisation. Introduced by Litterman (1986) and extended to high dimensions by Bańbura, Giannone and Reichlin (2010), it outperforms classical VAR on short series and high-dimensional macroeconomic forecasts.	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.