قارن الطرق

	اختبار جوهانسن المتين للتكامل المشترك	اختبار التكامل المشترك لإنجل-جرانجر
المجال	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model
سنة النشأة	1988–2010	1987
صاحب الطريقة	Johansen (1988, 1991); robust extensions by Cavaliere, Rahbek, Taylor (2010) and others	Robert F. Engle and Clive W. J. Granger
النوع	Cointegration rank test (robust variant)	Cointegration test
المصدر التأسيسي	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.
الأسماء البديلة	outlier-robust Johansen test, robust trace test, robust maximum eigenvalue test, robust cointegration rank test	EG cointegration test, Engle-Granger two-step method, residual-based cointegration test, EG test
ذات صلة	5	5
الملخص	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 Engle-Granger two-step method tests whether two or more non-stationary I(1) time series share a common stochastic trend — that is, whether a linear combination of them is stationary. If cointegration is confirmed, an error-correction model (ECM) can be estimated to capture both short-run dynamics and long-run equilibrium adjustment.