# Question on Stationary & Cointegration Test (Augmented Dickey Fuller & Engle Granger test)

I'm performing the stationary and cointegration test on stock prices.

What I'm confused is

2) Also, in ADF stationary test, I(1) means 'non-statioanry' and thus shows the auto correlation, while I(0) means stationary such that it is more of mean-reverting (rather than moving one way long). am I correct?

3) Is my test design logical?: first test the stationarity in ADF stationary test, and then if so, test cointegration in ADF cointegration test. If certain assets are not stationary in ADF stationary test, then put them through the Engle-Granger test to identify whether the cointegration relationship between assets exists.

Answers will be very much appreciated, and HUGE thanks in advnace :-)

1. The standard ADF test considers whether a univariate time series in integrated (denoted $I(1)$) or stationary (denoted $I(0)$). The null hypothesis is that the series is $I(1)$. If you reject the null, that favours the alternative of $I(0)$.
Meanwhile, the Engle-Granger procedure (which makes use of the ADF test on the way) considers whether a number of time series are cointegrated (denoted $CI(1,1)$) or not (denoted $CI(1,0)$). The null hypothesis is that the series are $CI(1,0)$, i.e. not cointegrated. If you reject the null, that favours the alternative of $CI(1,1)$.