1. weak stationarity
Part II METHODS FOR TESTING UNIT ROOTS
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- 3. THE DICKEY FULLER TEST
Part II METHODS FOR TESTING UNIT ROOTS Augmented Dickey-Fuller Test (ADF) Extensions to the Dickey-Fuller Test (DF) e.g “Pantula principle”, seasonal unit roots, structural breaks, fractional unit roots etc. Phillips-Perron Test (PP) Kwaitkowski-Phillips-Schmidt-Shin (KPSS) Elliot-Rothenberg-Stock point optimal (ERS) Ng-Perron test Etc. We only focus on the ADF. In all cases the basic idea is to search for the data generating process (DGP) from; Pure random walk Random walk with drift Random walk with drift and time trend 3. THE DICKEY FULLER TEST3.1 Pure random walk 
Where Subtracting Let Then The DGP is non-stationary if This parameterisation facilitates the use of the t-test. H0:  - Non-stationarity
H1:  – Stationarity
3.2 Random walk with drift (i) Test for stationarity alone For a DGP for random walk with drift, insert a constant/drift term (m) 
H0: - Non-stationarity
H1: - Stationary
(ii) Identifying joint significance of unit root and the drift term The main question here is whether nature generated the variable as a random walk with drift or not. This should be done by the following joint test H0:  - Non-stationarity
Failure to reject, whilst rejecting H0: while rejecting H0: and that  follows an asymptotic normal distribution.
3.3 Random walk with drift and trend (i) Test for stationarity alone For a DGP for random walk with drift, insert a constant/drift term (m) 
H0: - Non-stationarity
H1: - Stationary
follows distribution
(ii) Identifying joint significance of unit root and the time trend The main question here is whether nature generated the variable as a random walk with time trend or not. This should be done by the following joint test H0:  - Non-stationarity
Failure to reject H0: while rejecting H0: and that follows an asymptotic normal distribution.
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. The DGP is stationary if 
. Recall the Monte Carlo simulations