So sánh phương pháp

	Kiểm định Đồng tích dựa trên phần dư Phillips-Ouliaris	Kiểm định đồng tích hợp (Johansen / Engle-Granger)	Kiểm định nghiệm đơn vị Phillips-Perron (PP)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng
Họ	Hypothesis test	Regression model	Regression model
Năm ra đời	1990	1988	1988
Người khởi xướng	Peter Phillips & Sam Ouliaris	Engle & Granger (1987); Johansen (1988)	Peter C. B. Phillips & Pierre Perron
Loại	Residual-based nonparametric cointegration test	Time-series cointegration test	Unit-root test for stationarity
Công trình gốc	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.
Tên gọi khác	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
Liên quan	2	5	4
Tóm tắt	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.