Linganisha mbinu

	Kipimo cha Kufunga cha ARDL chenye Nguvu kwa Cointegration	Kipimo cha Uunganishaji wa Johansen na Kielelezo cha Mfumo wa Kurekebisha Makosa	Mfumo wa ARDL Usiohusisha Mstari (NARDL)
Nyanja	Ekonometriki	Fedha	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2019	1991	2014
Mwanzilishi	Sam, McNown & Goh	Søren Johansen	Shin, Yu & Greenwood-Nimmo
Aina	Cointegration test	Multivariate cointegration / vector error correction model	Nonlinear cointegration model
Chanzo asilia	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.
Majina mbadala	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
Zinazohusiana	3	3	5
Muhtasari	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.