Linganisha mbinu

	Kipimo cha Muungano wa Engle-Granger chenye Mkengeuko wa Kiunzi	Kipimo cha Vikomo vya ARDL (Kipimo cha Vikomo cha Pesaran)	Kipimo cha Uunganishaji wa Johansen na Kielelezo cha Mfumo wa Kurekebisha Makosa
Nyanja	Ekonometriki	Ekonometriki	Fedha
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	1996	2001	1991
Mwanzilishi	Gregory & Hansen (1996), extending Engle & Granger (1987)	Pesaran, Shin & Smith	Søren Johansen
Aina	Cointegration test with structural break	Cointegration test / Autoregressive distributed lag model	Multivariate cointegration / vector error correction model
Chanzo asilia	Gregory, A. W., & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics, 70(1), 99-126.	Pesaran, M. H., Shin, Y., & Smith, R. J. (2001). Bounds Testing Approaches to the Analysis of Level Relationships. Journal of Applied Econometrics, 16(3), 289–326.	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.
Majina mbadala	Gregory-Hansen cointegration test, cointegration with structural break, EG cointegration with regime shift, residual-based cointegration with break	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	Johansen test, VECM, vector error correction model, multivariate cointegration
Zinazohusiana	2	4	3
Muhtasari	The structural break Engle-Granger cointegration test, most commonly implemented via the Gregory-Hansen (1996) procedure, extends the classical Engle-Granger two-step test to allow for a single unknown structural break in the long-run cointegrating relationship. It tests whether two or more integrated series share a common stochastic trend even when that relationship may have shifted at some point in the sample.	The ARDL bounds test is an autoregressive distributed lag method that tests for a cointegrating (long-run level) relationship between time series, introduced by Pesaran, Shin and Smith in 2001. Unlike the Johansen procedure, it remains valid whether the variables are I(0), I(1) or a mix of the two, and it is more reliable than Johansen in small samples of roughly 30 to 80 observations.	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.