قارن الطرق

	اختبار جوهانسن المتين للتكامل المشترك	نموذج تصحيح الخطأ المتجهي (VECM)
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)	Multivariate time-series model
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	VECM, error correction VAR, cointegrated VAR, vector equilibrium correction model
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 Vector Error Correction Model extends the Vector Autoregression (VAR) framework to a system of variables that share one or more long-run equilibrium relationships. It jointly models short-run dynamics and the speed at which each variable corrects back toward equilibrium after a shock, making it the standard tool for analysing cointegrated multivariate time series.