Compara mètodes

	Test ERS de Raïtz Unitari Punt-Òptim	Prova de la unitat-arrel (ADF) augmentada de Dickey-Fuller	Prova d'arrel unitari de Phillips-Perron (PP)
Camp	Econometria	Econometria	Econometria
Família	Hypothesis test	Regression model	Regression model
Any d'origen	1996	1979	1988
Autor original	Elliott, Rothenberg & Stock	David A. Dickey & Wayne A. Fuller	Peter C. B. Phillips & Pierre Perron
Tipus	One-sided parametric unit-root test	Unit-root test for stationarity	Unit-root test for stationarity
Font seminal	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.	Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335–346.
Àlies	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	PP test, Phillips-Perron unit root test, Phillips-Perron birim kök testi
Relacionats	3	4	4
Resum	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 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.