Linganisha mbinu

	Ubora wa Utegemezi wa Viga (VAR)	Modeli ya ARMA (Autoregressive 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 E. P. Box and Gwilym M. Jenkins	Clive W. J. Granger
Aina	Multivariate time-series model	Time series 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	ARMA, Box-Jenkins model, autoregressive moving average, AR(p)MA(q)	Granger test, GC test, predictive causality test, Granger non-causality test
Zinazohusiana	5	5	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 ARMA(p,q) model describes a stationary time series as a combination of two components: an autoregressive part that regresses the current value on its own past p values, and a moving average part that accounts for past q error terms. It is the foundational framework of the Box-Jenkins methodology for univariate time series modelling and short-run forecasting.	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.