مقایسهٔ روش‌ها

	آزمون هم‌انباشتگی یوهانسن و مدل برداری تصحیح خطا	آزمون حدود ARDL (آزمون حدود پزاران)	مدل خودرگرسیون برداری (VAR)
حوزه	مالی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1991	2001	2005
پدیدآور	Søren Johansen	Pesaran, Shin & Smith	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
نوع	Multivariate cointegration / vector error correction model	Cointegration test / Autoregressive distributed lag model	Multivariate time-series model
منبع بنیادین	Johansen, S. (1991). Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models. Econometrica, 59(6), 1551-1580.	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.	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
نام‌های دیگر	Johansen test, VECM, vector error correction model, multivariate cointegration	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon
مرتبط	3	4	4
خلاصه	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 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.	Vector Autoregression is a multivariate time-series model that treats several interdependent series symmetrically, letting each variable depend on its own past values and the past values of all the others. It is the standard tool for capturing mutual causality and joint dynamics, developed in the modern multiple-time-series tradition treated by Lütkepohl (2005).