I have shown a tutorial video on ADF unit root test. In the video I have data generated and tested the unit root test and showed how the ADF test can behave when the assumptions are mis-specified.

In the time series among many following three equations are important. These equations are given as:

In all these equation the nature of time series will significantly differ depending upon the value $\rho $. If the value of $\left| \rho \right|<1$ then the series will be stationary, if $\left| \rho \right|=1$ then the series will be non-stationary and $\left| \rho \right|>1$ then the series will be explosive.

Here is my video post in which I have shown the exact process to perform an ADF Unit Root test with the real dataset. I have also shown what happens with the ADF values when we mis-judge the assumptions. Further below, I have shown the the step wise process with a flowchart diagram.

Exact process to do ADF Unit Root Test

A.1 See the p-value of ADF Test

A. 2 if p-value is less than level of significance usually 5% (reject the null hypothesis of unit root), thus the data is stationary. STOP the process

B. if p-value is greater than 5% level of significance

B.1 then see the p-value of estimated trend

B.2 if p-value < 5%, then the data has unit root. Stop the process and repeat the process on difference data from initial step.

C. if p-value > 5%, then the trend is insignificant, Go to step-2.

C.1 See the P value of ADF Test

C.2 if p-value is less than level of significance usually 5% (reject the null hypothesis of unit root), thus the data is stationary. STOP the process

D. if p-value is greater than 5% level of significance

D.1 then see the p-value of estimated intercept

D.2 if p-value < 5% for estimated intercept then the data has unit root. Stop the process and repeat the process on difference data from initial step.

E. if p-value > 5% for estimated intercept then the intercept is insignificant, Go to step-2.

E.1 See the P value of ADF Test

E.2 if p-value is less than level of significance usually 5% (reject the null hypothesis of unit root), thus the data is stationary. STOP the process

F. if p-value is greater than 5% level of significance then the data is non stationary. Stop the process and repeat the process on difference data from initial step.

Here, In a Diagram, I have shown a stylized picture.

Source: Pfaff, B. (2008) Analysis of Integrated and Cointegrated Time Series with R. Second Edition. Springer, New York