مقایسهٔ روش‌ها

	آزمون ریشه واحد بهینه نقطه‌ای ERS	آزمون DF-GLS: آزمون ریشه واحد دیک-فولر با روندزدایی GLS	آزمون ریشه واحد فیلیپس-پرون (PP)
حوزه	اقتصادسنجی	اقتصادسنجی	اقتصادسنجی
خانواده	Hypothesis test	Hypothesis test	Regression model
سال پیدایش	1996	1996	1988
پدیدآور	Elliott, Rothenberg & Stock	Elliott, Rothenberg & Stock	Peter C. B. Phillips & Pierre Perron
نوع	One-sided parametric unit-root test	One-sided t-test on GLS-detrended series	Unit-root test for stationarity
منبع بنیادین	Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813–836.	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.
نام‌های دیگر	ERS P-test, Point-Optimal Unit-Root Test, ERS PT statistic, ERS Nokta-Optimal Birim Kök 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
مرتبط	3	3	4
خلاصه	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 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.