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For the unit root test, what is the hypothesis being tested? Is it,
yt = pyt-1 + et
H0: p=1 v. Ha: p<1
or
Δyt = ayt-1 + et where a = p-1
H0: a=0 v. Ha: a<0

Thanks for any help!

Aren't those identical?

Yes, I was unclear. What I mean to ask is in the Dickey-Fuller Unit Root Test which hypothesis is being tested? a=0 or p=1.

If a=p-1 then they're the same.