So sánh phương pháp

	Kiểm định Đồng tích dựa trên phần dư Phillips-Ouliaris	Kiểm định đồng tích hợp (Johansen / Engle-Granger)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng
Họ	Hypothesis test	Regression model
Năm ra đời	1990	1988
Người khởi xướng	Peter Phillips & Sam Ouliaris	Engle & Granger (1987); Johansen (1988)
Loại	Residual-based nonparametric cointegration test	Time-series cointegration test
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.
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)
Liên quan	2	5
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).