مقایسهٔ روش‌ها

	SARIMAX	مدل آریما (میانگین متحرک یکپارچه خودرگرسیو)	مدل خودرگرسیون برداری بیزی (BVAR)	مدل فضای حالت (فیلتر کالمن)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	2015	2015	1986	1990
پدیدآور	Box & Jenkins (ARIMA framework); SARIMAX extension with exogenous regressors	Box & Jenkins (Box-Jenkins methodology)	Litterman (1986); Bańbura, Giannone & Reichlin (2010)	Harvey; Durbin & Koopman (state space treatment); Kalman filter
نوع	Seasonal time-series regression model	Univariate time-series model	Bayesian multivariate time-series model	State space time series model
منبع بنیادین	Hyndman, R. J. & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts.	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	Litterman, R. B. (1986). Forecasting with Bayesian Vector Autoregressions—Five Years of Experience. Journal of Business & Economic Statistics, 4(1), 25-38.	Harvey, A. C. (1990). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.
نام‌های دیگر	seasonal ARIMA with exogenous variables, SARIMA with regressors, ARIMAX, SARIMAX — Dışsal Değişkenli Mevsimsel ARIMA	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	BVAR, Bayesian vector autoregression, Minnesota prior VAR, Bayesian VAR (BVAR)	state space, Kalman filter, unobserved components model, Durum Uzayı Modeli (State Space / Kalman Filter)
مرتبط	4	5	5	4
خلاصه	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.	ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015).	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.	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.