I've recently start learning methods for determining whether or not time series are stationary. The first method I'm trying to learn is the 'Dickey-Fuller Test'. This test uses a time series modeled by an AR(1) process. The key is to find whether or not this process contains a unit root. If it contains a unit root, the series is said to be non-stationary.
While I'm understanding most of the derived equations, I'm inexperienced in hypothesis testing. Thus I'm struggling with the part when we actually implement the Dickey-Fuller test. There do not seem to be many resources that outline the iterative process for conducting the test.
I've outlined my question in full here:
https://i.stack.imgur.com/n9gOm.jpg
I appreciate any help!