مقایسهٔ روش‌ها

	آزمون ریشه واحد غیرخطی PP	آزمون ریشه واحد دیکی-فولر تعمیم‌یافته (ADF)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	1988 (base); 2000s (nonlinear extensions)	1979–1984
پدیدآور	Phillips & Perron (1988); nonlinear extensions by Kapetanios, Shin & Snell (2003) and related authors	Said & Dickey (1984); building on Dickey & Fuller (1979)
نوع	Unit root test with nonlinear adjustment	Hypothesis test (unit root)
منبع بنیادین	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335-346.	Said, S. E., & Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71(3), 599–607.
نام‌های دیگر	Nonlinear PP test, Nonlinear Phillips-Perron test, PP unit root test with nonlinear adjustment, nonlinear PP	ADF test, ADF unit root test, Dickey-Fuller test (augmented), Said-Dickey test
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 Augmented Dickey-Fuller test is the standard procedure for determining whether a univariate time series contains a unit root — that is, whether the series is non-stationary. It extends the original Dickey-Fuller test by including lagged difference terms that absorb serial correlation in the residuals, making the test valid for a wide range of time-series processes encountered in economics and finance.