مقایسهٔ روش‌ها

	آزمون کوانتگریشن مبتنی بر باقیمانده فیلیپس-اولیاریس	آزمون ریشه واحد فیلیپس-پرون (PP)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Hypothesis test	Regression model
سال پیدایش	1990	1988
پدیدآور	Peter Phillips & Sam Ouliaris	Peter C. B. Phillips & Pierre Perron
نوع	Residual-based nonparametric cointegration test	Unit-root test for stationarity
منبع بنیادین	Phillips, P. C. B., & Ouliaris, S. (1990). Asymptotic properties of residual based tests for cointegration. Econometrica, 58(1), 165–193.	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.
نام‌های دیگر	Phillips-Ouliaris Cointegration Test, PO Residual-Based Test, Residual-Based Cointegration Test, Phillips-Ouliaris Eşbütünleşme Testi	PP test, Phillips-Perron unit root test, Phillips-Perron birim kök testi
مرتبط	2	4
خلاصه	The Phillips-Ouliaris test, introduced by Phillips and Ouliaris in their 1990 Econometrica article, is a residual-based nonparametric procedure for testing the null hypothesis of no cointegration among a set of integrated I(1) time series. It corrects OLS residuals from a cointegrating regression for serial correlation and endogeneity using kernel-based long-run variance estimators, yielding two statistics—Z_alpha (variance-ratio) and Z_t (normalized coefficient)—whose asymptotic distributions are tabulated specifically for systems with multiple stochastic regressors.	The Phillips-Perron test, proposed by Peter Phillips and Pierre Perron in 1988, tests for a unit root in a time series, like the Augmented Dickey-Fuller test, but corrects for autocorrelation and heteroskedasticity in the errors non-parametrically rather than by adding lagged differences. It runs a simple Dickey-Fuller regression and then adjusts the test statistic using a long-run variance estimate, so the practitioner need not choose a lag length for the regression itself.