Linganisha mbinu

	Ubora wa Utegemezi wa Viga (VAR)	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Jaribio la Uasababishi wa Granger
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1980	1970	1969
Mwanzilishi	Christopher A. Sims	George Box and Gwilym Jenkins	Clive W. J. Granger
Aina	Multivariate time-series model	Time series forecasting model	Causality test (F-test on VAR)
Chanzo asilia	Sims, C. A. (1980). Macroeconomics and Reality. Econometrica, 48(1), 1–48.	Box, G. E. P., & Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424–438.
Majina mbadala	VAR, VAR model, vector autoregressive model, multivariate autoregression	ARIMA, Box-Jenkins model, integrated ARMA, ARIMA(p,d,q)	Granger test, GC test, predictive causality test, Granger non-causality test
Zinazohusiana	5	6	5
Muhtasari	Vector Autoregression is a multivariate time-series model in which each variable is regressed on its own lags and the lags of all other variables in the system. Originally proposed by Sims (1980) as a data-driven alternative to large structural macroeconomic models, VAR has become the standard workhorse for dynamic analysis in empirical economics and finance.	The ARIMA(p,d,q) model is the standard workhorse for univariate time series forecasting. It combines autoregressive terms (past values), differencing to induce stationarity, and moving average terms (past shocks) into a unified linear framework. Developed by Box and Jenkins (1970), it remains one of the most widely applied models in econometrics and applied statistics.	The Granger causality test is a statistical hypothesis test that determines whether past values of one time series help predict future values of another, beyond what that series' own past already explains. Introduced by Clive Granger in 1969, it is the standard approach for assessing predictive causality in VAR-based time-series analysis.