Linganisha mbinu

	Jaribio Imara la Mizizi ya Umoja la Phillips-Perron (PP)	Jaribio la Usimamishaji la KPSS
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1988 (base); 2000s–2010s (robust extensions)	1992
Mwanzilishi	Phillips & Perron (1988); robustification by Cavaliere & Taylor (2008) and related authors	Kwiatkowski, Phillips, Schmidt & Shin
Aina	Unit root / stationarity test	Stationarity test (reverse of unit-root tests)
Chanzo asilia	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.	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.
Majina mbadala	robust Phillips-Perron test, heteroskedasticity-robust PP test, nonparametric robust unit root test, robust PP	Kwiatkowski-Phillips-Schmidt-Shin test, stationarity test, KPSS durağanlık testi
Zinazohusiana	6	4
Muhtasari	The Robust Phillips-Perron unit root test extends the classical PP test by applying corrections — such as heteroskedasticity-consistent covariance estimation or wild-bootstrap critical values — that maintain valid inference when the error variance of a time series is non-constant or exhibits unconditional heteroskedasticity, conditions under which the standard PP test is severely size-distorted.	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.