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	Test granic ARDL (Pesaran Bounds Test)	Test kointegracji Johansena i wektorowy model korekty błędu	Model NARDL (Nonlinear Autoregressive Distributed Lag)
Dziedzina	Ekonometria	Finanse	Ekonometria
Rodzina	Regression model	Regression model	Regression model
Rok powstania	2001	1991	2014
Twórca	Pesaran, Shin & Smith	Søren Johansen	Shin, Yu & Greenwood-Nimmo
Typ	Cointegration test / Autoregressive distributed lag model	Multivariate cointegration / vector error correction model	Nonlinear cointegration model
Źródło pierwotne	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.	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.
Inne nazwy	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	Johansen test, VECM, vector error correction model, multivariate cointegration	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
Pokrewne	4	3	5
Podsumowanie	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.	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.