So sánh phương pháp

	Kiểm định giới hạn ARDL (Kiểm định giới hạn Pesaran)	Mô hình ARDL phi tuyến (NARDL)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model
Năm ra đời	2001	2014
Người khởi xướng	Pesaran, Shin & Smith	Shin, Yu & Greenwood-Nimmo
Loại	Cointegration test / Autoregressive distributed lag model	Nonlinear cointegration model
Công trình gốc	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.	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	Pesaran bounds test, bounds testing approach, ARDL cointegration test, ARDL Sınır Testi (Pesaran Bounds Test)	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
Liên quan	4	5
Tóm tắt	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 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.