השוואת שיטות

	מבחן קואינטגרציה מבוסס שיריים של פיליפס-אוליאריס	מבחן קואינטגרציה (יוהנסן / אנגל-גריינג'ר)	מבחן שורש יחידה פיליפס-פררון (PP)
תחום	אקונומטריקה	אקונומטריקה	אקונומטריקה
משפחה	Hypothesis test	Regression model	Regression model
שנת המקור	1990	1988	1988
הוגה השיטה	Peter Phillips & Sam Ouliaris	Engle & Granger (1987); Johansen (1988)	Peter C. B. Phillips & Pierre Perron
סוג	Residual-based nonparametric cointegration test	Time-series cointegration test	Unit-root test for stationarity
מקור מכונן	Phillips, P. C. B., & Ouliaris, S. (1990). Asymptotic properties of residual based tests for cointegration. Econometrica, 58(1), 165–193.	Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254.	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.
כינויים	Phillips-Ouliaris Cointegration Test, PO Residual-Based Test, Residual-Based Cointegration Test, Phillips-Ouliaris Eşbütünleşme Testi	Johansen cointegration test, Engle-Granger cointegration test, long-run equilibrium test, Eşbütünleşme Testi (Johansen/Engle-Granger)	PP test, Phillips-Perron unit root test, Phillips-Perron birim kök testi
קשורות	2	5	4
תקציר	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 cointegration test examines whether non-stationary time series that each contain a unit root share a stable long-run equilibrium relationship. The single-equation residual approach was introduced by Engle and Granger (1987) and the system-based rank approach by Johansen (1988).	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.