# Augmented Dickey-Fuller test null rejected. AR(1) in ARCH(1) p-value of 0.000

I am trying to model the logged returns of 5 different markets. When running the the Augmented Dickey-Fuller (ADF) tests on the logged market returns, the p-value is 0.000 for all markets regardless if the ADF includes 1) constant, 2) drift and constant or 3) neither constant or drift. Thus, it is assumed that none of these time series has no unit root, i.e. Y(t) is not dependent on Y(t-1), i.e. Y(t) is not autoregressive.

However, when running the ARMA(1,0) for the respective markets:
e.g. LN.Returns.GreenBonds = LN.Returns.GreenBonds(t-1) + e
the AR(1) parameter, LN.Returns.GreenBonds(t-1), has a p-value close to 0.000. How can this be the case when the ADF suggest that we do not have autoregressive time series?

Low p-values in an ADF test mean you reject the null hypothesis of presence of a unit root.

The ADF test does not tell whether the series are autoregressions or not. Instead, the ADF tests for presence of a unit root.