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	Modello di Correzione dell'Errore Vettoriale Non Lineare (Nonlinear VECM)	Il test ai limiti ARDL (ARDL Bounds Test)	Test di Cointegrazione di Johansen e Modello a Correzione d'Errore Vettoriale
Campo	Econometria	Econometria	Finanza
Famiglia	Regression model	Regression model	Regression model
Anno di origine	1989–1998	2001	1991
Ideatore	Granger & Lee (1989); Enders & Granger (1998)	Pesaran, Shin & Smith	Søren Johansen
Tipo	Nonlinear time-series model	Cointegration test / Autoregressive distributed lag model	Multivariate cointegration / vector error correction model
Fonte seminale	Enders, W., & Granger, C. W. J. (1998). Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics, 16(3), 304–311.	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.
Alias	nonlinear VECM, NVECM, threshold VECM, asymmetric VECM	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	Johansen test, VECM, vector error correction model, multivariate cointegration
Correlati	2	4	3
Sintesi	The Nonlinear VECM extends the standard linear VECM by allowing the speed of adjustment toward long-run equilibrium to differ depending on the sign, magnitude, or regime of deviations from that equilibrium. It captures asymmetric or threshold-driven dynamics in cointegrated time-series systems that a standard VECM would miss.	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.