مقایسهٔ روش‌ها

	آزمون هم‌انباشتگی (یوهانسن / انگل-گرنجر)	آزمون حدود ARDL (آزمون حدود پزاران)	مدل خودرگرسیون برداری (VAR)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	1988	2001	2005
پدیدآور	Engle & Granger (1987); Johansen (1988)	Pesaran, Shin & Smith	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition
نوع	Time-series cointegration test	Cointegration test / Autoregressive distributed lag model	Multivariate time-series model
منبع بنیادین	Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254.	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 cointegration test, Engle-Granger cointegration test, long-run equilibrium test, Eşbütünleşme Testi (Johansen/Engle-Granger)	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	5	4	4
خلاصه	The cointegration test examines whether non-stationary time series that each contain a unit root share a stable long-run equilibrium relationship. The single-equation residual approach was introduced by Engle and Granger (1987) and the system-based rank approach by Johansen (1988).	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).