مقایسهٔ روش‌ها

	آزمون ریشه واحد غیرخطی PP	مدل خودرگرسیون برداری غیرخطی (NARDL)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	1988 (base); 2000s (nonlinear extensions)	2014
پدیدآور	Phillips & Perron (1988); nonlinear extensions by Kapetanios, Shin & Snell (2003) and related authors	Shin, Yu & Greenwood-Nimmo
نوع	Unit root test with nonlinear adjustment	Nonlinear cointegration model
منبع بنیادین	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.
نام‌های دیگر	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
مرتبط	6	5
خلاصه	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.