विधियों की तुलना करें

	सुदृढ़ जोहानसेन सह-एकीकरण परीक्षण	सदिश त्रुटि सुधार मॉडल (VECM)
क्षेत्र	अर्थमिति	अर्थमिति
परिवार	Regression model	Regression model
उद्भव वर्ष	1988–2010	1987
प्रवर्तक	Johansen (1988, 1991); robust extensions by Cavaliere, Rahbek, Taylor (2010) and others	Robert F. Engle and Clive W. J. Granger
प्रकार	Cointegration rank test (robust variant)	Multivariate time-series model
मौलिक स्रोत	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.
उपनाम	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
संबंधित	5	5
सारांश	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.