# Interpreting results of an Augmented Dickey-Fuller test

I am running the 3 models of the ADF (Augmented Dickey Fuller) test on a (ln total fertility rate) variable. The results:

1. Intercept only: (lag difference = 0) at level; p-value for Z(t) = 0.9672.
This means that the variable is non-stationary, right? Coefficient of lnTFR.L1 = 0.00072 2-
I read that if the coefficient of L1 is not negative, the model is invalid. What does that mean?

2. Intercept + trend: (lag difference = 0) at level; p-value for Z(t) = 0.9409.
Does this mean that the variable TFR is also non-stationary when including trend? Coefficient of lnTFR.L1= -0.04623; now the coefficient is negative, so is the model valid?

3. No intercept + no trend: (lag difference=0) at level; the test statistic (12.762) is much higher than the 1% critical value (2.642) and 5% critical value (1.95). Does this mean that the variable is stationary with no trend and intercept? In this case what should I do?

When I tried a lag difference = 1 at level I found that the variable became stationary in the model intercept + trend! Should I take the first difference, or only conclude that the variable at level is stationary with 1 lag difference? Thanks! :)

• Does it make sense to not have an intercept? Does it vary around 0, or does it start at something completely different? If it doesn't make sense to exclude an intercept, that test specification isn't really relevant. – hejseb May 26 '14 at 8:24