مقایسهٔ روش‌ها

	آزمون ریشه واحد فیلیپس-پرون (PP)	مدل آریما (میانگین متحرک یکپارچه خودرگرسیو)	آزمون هم‌انباشتگی (یوهانسن / انگل-گرنجر)	آزمون ایستایی KPSS
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model	Regression model	Regression model
سال پیدایش	1988	2015	1988	1992
پدیدآور	Peter C. B. Phillips & Pierre Perron	Box & Jenkins (Box-Jenkins methodology)	Engle & Granger (1987); Johansen (1988)	Kwiatkowski, Phillips, Schmidt & Shin
نوع	Unit-root test for stationarity	Univariate time-series model	Time-series cointegration test	Stationarity test (reverse of unit-root tests)
منبع بنیادین	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.	Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1–3), 159–178.
نام‌های دیگر	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)	Kwiatkowski-Phillips-Schmidt-Shin test, stationarity test, KPSS durağanlık testi
مرتبط	4	5	5	4
خلاصه	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).	The KPSS test, introduced by Kwiatkowski, Phillips, Schmidt and Shin in 1992, tests the null hypothesis that a series is stationary against the alternative that it contains a unit root — the reverse of the ADF and Phillips-Perron tests. By flipping the burden of proof, it is designed to be used alongside unit-root tests so that the two can confirm one another and expose ambiguous, borderline cases.