So sánh phương pháp

	Kiểm định giới hạn ARDL mạnh mẽ cho đồng tích hợp	Kiểm định giới hạn ARDL (Kiểm định giới hạn Pesaran)	Kiểm định Đồng tích hợp Johansen và Mô hình Hiệu chỉnh Sai số Vector	Mô hình ARDL phi tuyến (NARDL)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Tài chính	Kinh tế lượng
Họ	Regression model	Regression model	Regression model	Regression model
Năm ra đời	2019	2001	1991	2014
Người khởi xướng	Sam, McNown & Goh	Pesaran, Shin & Smith	Søren Johansen	Shin, Yu & Greenwood-Nimmo
Loại	Cointegration test	Cointegration test / Autoregressive distributed lag model	Multivariate cointegration / vector error correction model	Nonlinear cointegration model
Công trình gốc	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.	Shin, Y., Yu, B., & Greenwood-Nimmo, M. (2014). Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework. In R. C. Sickles & W. C. Horrace (Eds.), Festschrift in Honor of Peter Schmidt: Econometric Methods and Applications (pp. 281–314). Springer.
Tên gọi khác	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	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
Liên quan	3	4	3	5
Tóm tắt	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.	The Nonlinear ARDL (NARDL) model extends the linear ARDL bounds-testing framework to allow asymmetric long-run and short-run relationships. By decomposing the regressor into cumulative positive and negative partial sums, it tests whether increases and decreases in a variable exert different effects on the outcome — a feature especially relevant in financial and energy economics where positive and negative shocks rarely cancel out symmetrically.