مقایسهٔ روش‌ها

	آزمون کران مقیدسازی ARDL استوار	آزمون حدود ARDL (آزمون حدود پزاران)	آزمون هم‌انباشتگی یوهانسن و مدل برداری تصحیح خطا
حوزه	اقتصادسنجی	اقتصادسنجی	مالی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	2019	2001	1991
پدیدآور	Sam, McNown & Goh	Pesaran, Shin & Smith	Søren Johansen
نوع	Cointegration test	Cointegration test / Autoregressive distributed lag model	Multivariate cointegration / vector error correction model
منبع بنیادین	Sam, C. Y., McNown, R., & Goh, S. K. (2019). An augmented autoregressive distributed lag bounds test for cointegration. Economic Modelling, 80, 130-141.	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.
نام‌های دیگر	Robust ARDL, Robust bounds testing approach, Sam-McNown-Goh bounds test, Bootstrap ARDL bounds test	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	Johansen test, VECM, vector error correction model, multivariate cointegration
مرتبط	3	4	3
خلاصه	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 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.