Linganisha mbinu

	Kielelezo cha Utegemezi wa Kujirudia kwa Kiasi Kidogo (NARDL)	Kipimo cha Vikomo vya ARDL (Kipimo cha Vikomo cha Pesaran)	Kipimo cha Granger Causality
Nyanja	Ekonometriki	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model	Regression model
Mwaka wa asili	2014	2001	1969
Mwanzilishi	Shin, Yu, and Greenwood-Nimmo	Pesaran, Shin & Smith	Clive W. J. Granger
Aina	Nonlinear cointegration model	Cointegration test / Autoregressive distributed lag model	Time-series predictive causality test
Chanzo asilia	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.	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.	Granger, C. W. J. (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Econometrica, 37(3), 424-438.
Majina mbadala	NARDL, nonlinear ARDL, asymmetric ARDL, nonlinear bounds test	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	Granger causality test, Granger non-causality test, predictive causality test, Granger Nedensellik Testi
Zinazohusiana	4	4	5
Muhtasari	The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing an explanatory variable into its positive and negative partial sums, it tests whether increases and decreases in a regressor have different effects on the dependent variable — a feature that linear cointegration methods cannot capture.	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 Granger causality test, introduced by Clive W. J. Granger in 1969, assesses whether the past values of one time series help predict another beyond what the latter's own past already explains. It defines causality in a strictly predictive sense rather than as a structural or physical cause.