I have yearly data. When I do a Dickey-Fuller test it gives me insignificant results, indicating that the series are non-stationary. After differencing them the DFT tells me they are now significant and stationary.
When using an ACF/PACF plot on the original series it is obvious that an AR(1) process should be used.
When plotting ACF/PACF for the first difference I can't make that same inference again because there is no significant spike in the ACF.