For my time-series regression, I am regressing the difference in variable x on a difference in variable y. Before proceeding, I want to check for stationarity of my variables. Regressing d.x (difference in x) over L.d.x (lag of the difference in x), I get a coefficient of $-0.9995261$ and a 95% interval: $[-1.000654, -0.9983979]$. As far as I remember, the abs value of the coefficient (and the values in the interval) must be less than 1 for us to be sure of the stationarity, which is not the case here. So I conducted a Dickey-Fuller test (all of this in Stata) and got the following results:
Interpolated Dickey-Fuller Test Statistic | 1% Critical Value | 5% Critical Value | 10% Critical Value Z(t) -3474.557 | -3.430 | -2.860 | -2.570 MacKinnon approximate p-value for Z(t) = 0.0000
I am confused because they very strongly suggest that there is no unit root, whereas I expected a close call. Is this because I have ~5000 observations? Or am I wrong, and the condition for the unit root is a coefficient in excess of 1, not its absolute value in excess of one?