Dickey-Fuller Test

Definition

The Dikey-Fuller test is used to test the presence of unit root in an AR time series model.

Consider an AR(1) model $y_t=\rho y_{t-1}+e_t$ The null hypothesis is set as $H_0:\rho =1,H_1:\rho <1$

Augmented Dickey-Fuller Test

Consider an AR(p) model $y_t=\alpha +{\theta }_1{y}_{t-1}+{\theta }_2{y}_{t-2}+\cdots ++{\theta }_p{y}_{t-p}+e_t$ The null hypothesis is set as $H_0:{\theta }_1={\theta }_2=\cdots ={\theta }_p=0$

ADF-GLS Test (ERS Test)

Remove constant and trend effects from the data and perform the ADF test on the residuals.