Krahasoni metodat

	SARIMAX	Model ARIMA (Autoregressive Integrated Moving Average)	Vektori Autoregresiv Bayesian (BVAR)	Model i Hapësirës së Gjendjeve (Filtri Kalman)
Fusha	Ekonometri	Ekonometri	Ekonometri	Ekonometri
Familja	Regression model	Regression model	Regression model	Regression model
Viti i origjinës	2015	2015	1986	1990
Krijuesi	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
Lloji	Seasonal time-series regression model	Univariate time-series model	Bayesian multivariate time-series model	State space time series model
Burimi themelues	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.
Emërtime të tjera	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)
Të lidhura	4	5	5	4
Përmbledhja	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.