Σύγκριση μεθόδων

	Μη γραμμική συν-ολοκλήρωση Engle-Granger	Δοκιμή Συνολοκλήρωσης κατά Johansen και Μοντέλο Διόρθωσης Σφαλμάτων Διανυσμάτων	Μοντέλο μη γραμμικού ARDL (NARDL)
Πεδίο	Οικονομετρία	Χρηματοοικονομικά	Οικονομετρία
Οικογένεια	Regression model	Regression model	Regression model
Έτος προέλευσης	1998-2006	1991	2014
Δημιουργός	Kapetanios, Shin & Snell; Enders & Granger	Søren Johansen	Shin, Yu & Greenwood-Nimmo
Τύπος	Cointegration test	Multivariate cointegration / vector error correction model	Nonlinear cointegration model
Θεμελιώδης πηγή	Kapetanios, G., Shin, Y., & Snell, A. (2006). Testing for cointegration in nonlinear smooth transition error correction models. Econometric Theory, 22(2), 279-303.	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.	Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In R. C. Sickles & W. C. Horrace (Eds.), Festschrift in Honor of Peter Schmidt: Econometric Methods and Applications (pp. 281–314). Springer.
Εναλλακτικές ονομασίες	nonlinear cointegration, threshold cointegration, KSS cointegration, ESTAR cointegration	Johansen test, VECM, vector error correction model, multivariate cointegration	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
Συναφείς	3	3	5
Σύνοψη	Nonlinear Engle-Granger cointegration extends the classical two-step Engle-Granger procedure to detect long-run equilibria where adjustment toward the equilibrium is nonlinear — for example, faster above than below a threshold, or governed by a smooth transition mechanism. It is widely applied in financial economics, purchasing power parity tests, and commodity price analysis.	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.	The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing the regressor into cumulative positive and negative partial sums, it tests whether increases and decreases in a variable exert different effects on the outcome — a feature especially relevant in financial and energy economics where positive and negative shocks rarely cancel out symmetrically.