विधियों की तुलना करें

	DF-GLS परीक्षण: GLS-डिट्रेंडेड डिकी-फुलर यूनिट-रूट परीक्षण	ऑग्मेंटेड डिकी-फुलर (एडीएफ) यूनिट-रूट टेस्ट	ERS बिंदु-इष्टतम इकाई-मूल परीक्षण	KPSS स्थिरता परीक्षण
क्षेत्र	अर्थमिति	अर्थमिति	अर्थमिति	अर्थमिति
परिवार	Hypothesis test	Regression model	Hypothesis test	Regression model
उद्भव वर्ष	1996	1979	1996	1992
प्रवर्तक	Elliott, Rothenberg & Stock	David A. Dickey & Wayne A. Fuller	Elliott, Rothenberg & Stock	Kwiatkowski, Phillips, Schmidt & Shin
प्रकार	One-sided t-test on GLS-detrended series	Unit-root test for stationarity	One-sided parametric unit-root test	Stationarity test (reverse of unit-root tests)
मौलिक स्रोत	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.	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.
उपनाम	Elliott-Rothenberg-Stock test, ERS unit-root test, GLS-detrended Dickey-Fuller test, DF-GLS birim kök testi	ADF test, Dickey-Fuller test, unit root test, Genişletilmiş Dickey-Fuller testi	ERS P-test, Point-Optimal Unit-Root Test, ERS PT statistic, ERS Nokta-Optimal Birim Kök Testi	Kwiatkowski-Phillips-Schmidt-Shin test, stationarity test, KPSS durağanlık testi
संबंधित	3	4	3	4
सारांश	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 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 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 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.