So sánh phương pháp

	Kiểm định nghiệm đơn vị Phillips-Perron (PP)	Mô hình ARIMA (Autoregressive Integrated Moving Average)	Kiểm định đồng tích hợp (Johansen / Engle-Granger)
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model	Regression model
Năm ra đời	1988	2015	1988
Người khởi xướng	Peter C. B. Phillips & Pierre Perron	Box & Jenkins (Box-Jenkins methodology)	Engle & Granger (1987); Johansen (1988)
Loại	Unit-root test for stationarity	Univariate time-series model	Time-series cointegration test
Công trình gốc	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.	Box, G. E. P., Jenkins, G. M., Reinsel, G. C. & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley. ISBN: 978-1118675021	Johansen, S. (1988). Statistical Analysis of Cointegration Vectors. Journal of Economic Dynamics and Control, 12(2-3), 231-254.
Tên gọi khác	PP test, Phillips-Perron unit root test, Phillips-Perron birim kök testi	Box-Jenkins model, ARIMA(p,d,q), ARIMA Modeli	Johansen cointegration test, Engle-Granger cointegration test, long-run equilibrium test, Eşbütünleşme Testi (Johansen/Engle-Granger)
Liên quan	4	5	5
Tóm tắt	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.	ARIMA is a univariate time-series forecasting model that combines autoregressive, integrated (differencing), and moving-average components to predict a single continuous series from its own past. It is the centrepiece of the Box-Jenkins methodology set out in Box, Jenkins, Reinsel & Ljung's Time Series Analysis (5th ed., 2015).	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).