You can see the beta on the AR(t-1) and then do a hypothesis test that AR(t-1) = 1, if it is, then you also have a unit root.
Sorry, it should be: Basically it starts from AR(1) till all Null hypotheses(for each lag) can not rejected. Otherwise, it will be an endless loop.
(1) random walk: x(t)=x(t-1)+e(t). (2) covariance stationary: y(t)=e(t), where y(t)=x(t)-x(t-1). I think this is the same thing presented in two diff forms. Since (1) is not useful, why is (2) useful? Any help is welcome.
all you’re doing in going from (1) to (2) is reworking the formula so that b1 = 0 and b0 = 0, thus resulting in a mean reverting level b0 / (1-b1) of 0, as opposed to an undefined result (something divided by 0).