مقایسهٔ روش‌ها

	آزمون کرانه‌های ARDL با پارامترهای متغیر با زمان	آزمون حدود ARDL (آزمون حدود پزاران)	مدل خودرگرسیون برداری غیرخطی (NARDL)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	2010s	2001	2014
پدیدآور	Extension of Pesaran, Shin & Smith (2001); TVP variant developed in applied time-series literature ca. 2010s	Pesaran, Shin & Smith	Shin, Yu & Greenwood-Nimmo
نوع	Cointegration / bounds test with time-varying coefficients	Cointegration test / Autoregressive distributed lag model	Nonlinear cointegration model
منبع بنیادین	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.	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.	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.
نام‌های دیگر	TVP-ARDL bounds test, time-varying ARDL cointegration, TVP bounds testing approach, dynamic ARDL bounds test	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
مرتبط	2	4	5
خلاصه	The time-varying parameter ARDL bounds test extends the classic Pesaran-Shin-Smith (2001) bounds testing framework by allowing regression coefficients to evolve continuously over time. It detects whether a long-run cointegrating relationship between variables exists and whether that relationship has been stable or shifting across the sample period.	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 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.