Linganisha mbinu

	Kipimo cha ushirikiano (Johansen / Engle-Granger)	Mfumo wa ARIMA (Autoregressive Integrated Moving Average)	Kipimo cha Granger Causality
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1988	2015	1969
Mwanzilishi	Engle & Granger (1987); Johansen (1988)	Box & Jenkins (Box-Jenkins methodology)	Clive W. J. Granger
Aina	Time-series cointegration test	Univariate time-series model	Time-series predictive causality test
Chanzo asilia	Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254.	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	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424-438.
Majina mbadala	Johansen cointegration test, Engle-Granger cointegration test, long-run equilibrium test, Eşbütünleşme Testi (Johansen/Engle-Granger)	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	Granger causality test, Granger non-causality test, predictive causality test, Granger Nedensellik Testi
Zinazohusiana	5	5	5
Muhtasari	The cointegration test examines whether non-stationary time series that each contain a unit root share a stable long-run equilibrium relationship. The single-equation residual approach was introduced by Engle and Granger (1987) and the system-based rank approach by Johansen (1988).	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).	The Granger causality test, introduced by Clive W. J. Granger in 1969, assesses whether the past values of one time series help predict another beyond what the latter's own past already explains. It defines causality in a strictly predictive sense rather than as a structural or physical cause.