مقایسهٔ روش‌ها

	آزمون ریشه واحد فیلیپس-پرون (PP) مقاوم	آزمون ریشه واحد غیرخطی PP
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	1988 (base); 2000s–2010s (robust extensions)	1988 (base); 2000s (nonlinear extensions)
پدیدآور	Phillips & Perron (1988); robustification by Cavaliere & Taylor (2008) and related authors	Phillips & Perron (1988); nonlinear extensions by Kapetanios, Shin & Snell (2003) and related authors
نوع	Unit root / stationarity test	Unit root test with nonlinear adjustment
منبع بنیادین	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335-346.
نام‌های دیگر	robust Phillips-Perron test, heteroskedasticity-robust PP test, nonparametric robust unit root test, robust PP	Nonlinear PP test, Nonlinear Phillips-Perron test, PP unit root test with nonlinear adjustment, nonlinear PP
مرتبط	6	6
خلاصه	The Robust Phillips-Perron unit root test extends the classical PP test by applying corrections — such as heteroskedasticity-consistent covariance estimation or wild-bootstrap critical values — that maintain valid inference when the error variance of a time series is non-constant or exhibits unconditional heteroskedasticity, conditions under which the standard PP test is severely size-distorted.	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.