So sánh phương pháp

	Kiểm định nghiệm đơn vị PP phi tuyến	Mô hình ARDL phi tuyến (NARDL)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model
Năm ra đời	1988 (base); 2000s (nonlinear extensions)	2014
Người khởi xướng	Phillips & Perron (1988); nonlinear extensions by Kapetanios, Shin & Snell (2003) and related authors	Shin, Yu & Greenwood-Nimmo
Loại	Unit root test with nonlinear adjustment	Nonlinear cointegration model
Công trình gốc	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335-346.	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	Nonlinear PP test, Nonlinear Phillips-Perron test, PP unit root test with nonlinear adjustment, nonlinear PP	NARDL, nonlinear bounds test, asymmetric ARDL, asymmetric cointegration model
Liên quan	6	5
Tóm tắt	The Nonlinear Phillips-Perron unit root test extends the classic PP test by allowing the adjustment toward equilibrium to follow a nonlinear path — such as a smooth transition or threshold mechanism — rather than assuming a constant linear speed of adjustment. This makes it more powerful when the true data-generating process involves regime-dependent or asymmetric mean-reversion dynamics.	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.