مقایسهٔ روش‌ها

	مدل خودرگرسیون برداری (VAR)	آزمون حدود ARDL (آزمون حدود پزاران)	مدل تصحیح خطای برداری (VECM)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model
سال پیدایش	2005	2001	1987
پدیدآور	Lütkepohl (textbook treatment); Sims (1980) macroeconometric tradition	Pesaran, Shin & Smith	Engle & Granger
نوع	Multivariate time-series model	Cointegration test / Autoregressive distributed lag model	Multivariate time-series model
منبع بنیادین	Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.	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.	Engle, R. F. & Granger, C. W. J. (1987). Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55(2), 251-276.
نام‌های دیگر	vector autoregression, VAR, VAR Modeli (Vektör Otoregresyon), vektör otoregresyon	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	vector error correction model, error correction model, cointegration model, VECM (Vektör Hata Düzeltme Modeli)
مرتبط	4	4	4
خلاصه	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).	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 Vector Error Correction Model is a multivariate time-series model for cointegrated series that captures both their short-run dynamics and their long-run equilibrium relationship. It was introduced by Engle and Granger in 1987 as part of the cointegration and error-correction framework.