Linganisha mbinu

	Kipimo cha Uthabiti cha Ukozi wa Johansen	Kipimo thabiti cha kuunganishwa kwa Engle-Granger
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1988–2010	1987 (base); robust variants 2000s–2020s
Mwanzilishi	Johansen (1988, 1991); robust extensions by Cavaliere, Rahbek, Taylor (2010) and others	Engle & Granger (1987); robust extensions by subsequent authors including Hao & Shaffer and others
Aina	Cointegration rank test (robust variant)	Cointegration test
Chanzo asilia	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551–1580.	Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276.
Majina mbadala	outlier-robust Johansen test, robust trace test, robust maximum eigenvalue test, robust cointegration rank test	robust EG cointegration, outlier-robust cointegration test, robust two-step cointegration, robust EG test
Zinazohusiana	5	5
Muhtasari	The Robust Johansen Cointegration test extends the classical Johansen (1988, 1991) likelihood-ratio framework for determining the cointegrating rank of a multivariate I(1) system to settings where standard Gaussian assumptions fail — in particular when the data exhibit outliers, fat-tailed innovations, or conditional heteroskedasticity. Robust modifications adjust residuals, re-weight observations, or bootstrap critical values so that rank inference remains valid under these violations.	The Robust Engle-Granger cointegration test adapts the classic two-step Engle-Granger procedure to withstand outliers, heavy-tailed error distributions, and additive noise that can severely distort standard residual-based cointegration inference. By substituting robust regression and robust unit-root testing for classical OLS and ADF steps, it yields reliable conclusions about long-run equilibrium relationships even when the data contain anomalous observations.