مقایسهٔ روش‌ها

	هم‌انباشتگی انگل-گرنجر با پارامترهای متغیر با زمان	آزمون هم‌انباشتگی یوهانسن و مدل برداری تصحیح خطا
حوزه	اقتصادسنجی	مالی
خانواده	Regression model	Regression model
سال پیدایش	1987/1999	1991
پدیدآور	Engle & Granger (1987) for cointegration; Park & Hahn (1999) for TVP extension	Søren Johansen
نوع	Time-series cointegration model	Multivariate cointegration / vector error correction model
منبع بنیادین	Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276.	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.
نام‌های دیگر	TVP Engle-Granger cointegration, time-varying cointegration, TVP-EG cointegration, varying-coefficient cointegration	Johansen test, VECM, vector error correction model, multivariate cointegration
مرتبط	3	3
خلاصه	Time-varying parameter (TVP) Engle-Granger cointegration extends the classical two-step Engle-Granger framework by allowing the long-run relationship between integrated series to evolve over time. Instead of assuming a fixed cointegrating vector, the cointegrating coefficients are modelled as stochastic processes — typically via a random walk — and estimated with the Kalman filter or related state-space methods.	The Johansen procedure is a multivariate cointegration framework, introduced by Søren Johansen in 1991, that tests for long-run equilibrium relationships among several I(1) time series. It determines how many cointegrating vectors link the series and then builds a Vector Error Correction Model (VECM) to describe the short-run dynamics around that equilibrium.