Linganisha mbinu

	Kipimo cha Mizizi Mfumo cha Robust Augmented Dickey-Fuller	Kipimo cha Mizizi ya Muungano cha Augmented Dickey-Fuller (ADF)
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1996-2001	1979–1984
Mwanzilishi	Ng and Perron (2001); Elliott, Rothenberg, and Stock (1996)	Said & Dickey (1984); building on Dickey & Fuller (1979)
Aina	Unit root / stationarity test	Hypothesis test (unit root)
Chanzo asilia	Ng, S., and Perron, P. (2001). Lag length selection and the construction of unit root tests with good size and power. Econometrica, 69(6), 1519-1554.	Said, S. E., & Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71(3), 599–607.
Majina mbadala	robust ADF test, HAC-corrected ADF, heteroscedasticity-robust unit root test, GLS-detrended ADF	ADF test, ADF unit root test, Dickey-Fuller test (augmented), Said-Dickey test
Zinazohusiana	6	5
Muhtasari	The Robust ADF unit root test extends the classical ADF procedure with improvements that correct for size distortions arising from heteroscedastic or serially correlated errors, and from poor lag-length selection. Drawing on GLS detrending (Elliott, Rothenberg, and Stock 1996) and modified information criteria (Ng and Perron 2001), it delivers reliable size and power in the presence of non-standard error processes common in macroeconomic and financial time series.	The Augmented Dickey-Fuller test is the standard procedure for determining whether a univariate time series contains a unit root — that is, whether the series is non-stationary. It extends the original Dickey-Fuller test by including lagged difference terms that absorb serial correlation in the residuals, making the test valid for a wide range of time-series processes encountered in economics and finance.