Linganisha mbinu

	Kointeregesheni Isiyo ya Mstari ya Engle-Granger	Kipimo cha Vikomo vya ARDL (Kipimo cha Vikomo cha Pesaran)	Kipimo cha Uunganishaji wa Johansen na Kielelezo cha Mfumo wa Kurekebisha Makosa	Mfumo wa ARDL Usiohusisha Mstari (NARDL)
Nyanja	Ekonometriki	Ekonometriki	Fedha	Ekonometriki
Familia	Regression model	Regression model	Regression model	Regression model
Mwaka wa asili	1998-2006	2001	1991	2014
Mwanzilishi	Kapetanios, Shin & Snell; Enders & Granger	Pesaran, Shin & Smith	Søren Johansen	Shin, Yu & Greenwood-Nimmo
Aina	Cointegration test	Cointegration test / Autoregressive distributed lag model	Multivariate cointegration / vector error correction model	Nonlinear cointegration model
Chanzo asilia	Kapetanios, G., Shin, Y., & Snell, A. (2006). Testing for cointegration in nonlinear smooth transition error correction models. Econometric Theory, 22(2), 279-303.	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.
Majina mbadala	nonlinear cointegration, threshold cointegration, KSS cointegration, ESTAR cointegration	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
Zinazohusiana	3	4	3	5
Muhtasari	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 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.