مقایسهٔ روش‌ها

	هم‌انباشتگی غیرخطی انگل-گرنجر	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	1998-2006	2001	1991
پدیدآور	Kapetanios, Shin & Snell; Enders & Granger	Pesaran, Shin & Smith	Søren Johansen
نوع	Cointegration test	Cointegration test / Autoregressive distributed lag model	Multivariate cointegration / vector error correction model
منبع بنیادین	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.
نام‌های دیگر	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
مرتبط	3	4	3
خلاصه	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.