Methoden vergleichen

	ERS Point-Optimal Unit-Root Test	Augmented-Dickey-Fuller (ADF)-Test auf Einheitswurzel	DF-GLS-Test: Dickey-Fuller-GLS-Test auf Einheitswurzeln nach Trendbereinigung	Phillips-Perron (PP) Einheitswurzel-Test
Fachgebiet	Ökonometrie	Ökonometrie	Ökonometrie	Ökonometrie
Familie	Hypothesis test	Regression model	Hypothesis test	Regression model
Entstehungsjahr	1996	1979	1996	1988
Urheber	Elliott, Rothenberg & Stock	David A. Dickey & Wayne A. Fuller	Elliott, Rothenberg & Stock	Peter C. B. Phillips & Pierre Perron
Typ	One-sided parametric unit-root test	Unit-root test for stationarity	One-sided t-test on GLS-detrended series	Unit-root test for stationarity
Wegweisende Quelle	Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813–836.	Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366a), 427–431.	Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813–836.	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.
Aliasnamen	ERS P-test, Point-Optimal Unit-Root Test, ERS PT statistic, ERS Nokta-Optimal Birim Kök Testi	ADF test, Dickey-Fuller test, unit root test, Genişletilmiş Dickey-Fuller testi	Elliott-Rothenberg-Stock test, ERS unit-root test, GLS-detrended Dickey-Fuller test, DF-GLS birim kök testi	PP test, Phillips-Perron unit root test, Phillips-Perron birim kök testi
Verwandt	3	4	3	4
Zusammenfassung	The Elliott-Rothenberg-Stock (ERS) Point-Optimal test, introduced in their landmark 1996 Econometrica paper, is a near-efficient parametric procedure for testing whether a univariate time series contains a unit root. By first applying GLS detrending at a carefully chosen local-to-unity value and then computing a likelihood-ratio-type statistic, it achieves power close to the Gaussian power envelope—making it one of the most powerful unit-root tests available to applied econometricians.	The Augmented Dickey-Fuller (ADF) test is the most widely used test for a unit root — that is, for whether a time series is non-stationary and must be differenced before modelling. Introduced by David Dickey and Wayne Fuller in 1979 and extended by Said and Dickey in 1984 to series with higher-order autocorrelation, it regresses the change in the series on its lagged level plus lagged differences and asks whether the lagged-level coefficient is zero.	The DF-GLS test, introduced by Elliott, Rothenberg, and Stock (1996), is a modified augmented Dickey-Fuller procedure that applies generalized least squares (GLS) detrending before the standard unit-root regression. By removing deterministic components under a local alternative rather than the null hypothesis, the test achieves near-optimal power for detecting stationarity in time series, making it the preferred unit-root test in applied econometrics when a trend or intercept is present.	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.