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	Test dei limiti ARDL robusto per la cointegrazione	Test di Cointegrazione di Johansen e Modello a Correzione d'Errore Vettoriale	Modello ARDL Non Lineare (NARDL)
Campo	Econometria	Finanza	Econometria
Famiglia	Regression model	Regression model	Regression model
Anno di origine	2019	1991	2014
Ideatore	Sam, McNown & Goh	Søren Johansen	Shin, Yu & Greenwood-Nimmo
Tipo	Cointegration test	Multivariate cointegration / vector error correction model	Nonlinear cointegration model
Fonte seminale	Sam, C. Y., McNown, R., & Goh, S. K. (2019). An augmented autoregressive distributed lag bounds test for cointegration. Economic Modelling, 80, 130-141.	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.
Alias	Robust ARDL, Robust bounds testing approach, Sam-McNown-Goh bounds test, Bootstrap ARDL bounds test	Johansen test, VECM, vector error correction model, multivariate cointegration	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
Correlati	3	3	5
Sintesi	The Robust ARDL bounds test is an augmented version of the Pesaran-Shin-Smith (2001) ARDL bounds testing approach that resolves its two key weaknesses: size distortion under mixed integration orders and the degenerate-case problem. It introduces three separate test statistics — an overall F-test and two new Wald statistics for the dependent and independent variables — evaluated against bootstrap-generated critical values.	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.