قارن الطرق

	اختبار جوهانسن للتكامل المشترك غير الخطي	نموذج تصحيح الخطأ المتجهي (VECM)
المجال	الاقتصاد القياسي	الاقتصاد القياسي
العائلة	Regression model	Regression model
سنة النشأة	2001	1987
صاحب الطريقة	Breitung (2001), building on Johansen (1988, 1991)	Robert F. Engle and Clive W. J. Granger
النوع	Nonparametric rank-based cointegration test	Multivariate time-series model
المصدر التأسيسي	Breitung, J. (2001). Rank tests for nonlinear cointegration. Journal of Business and Economic Statistics, 19(3), 331-340.	Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276.
الأسماء البديلة	nonlinear cointegration test, threshold Johansen cointegration, rank test for nonlinear cointegration, nonlinear VECM cointegration	VECM, error correction VAR, cointegrated VAR, vector equilibrium correction model
ذات صلة	3	5
الملخص	Nonlinear Johansen cointegration extends the classical Johansen framework to detect long-run equilibrium relationships among integrated time series when the adjustment process is nonlinear. Using rank-based transformations, the approach tests for cointegration without assuming a linear error-correction mechanism, making it suitable for economic relationships characterized by asymmetric or threshold dynamics.	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.