I'm trying to determine the AR and MA of a time series by looking at the ACF/PACF plots but they doesn't look like the classic examples of the textbooks.
it has 264 monthly values of a stock index from 2000 to 2022. The series is not stationary so I take a diff and then plot acf/pacf. As you can see the first and second lags of either plots are not significant but the third lag is. I don't know how to interpret this.
Thanks for your help! Edited just to add some extra info (commands are from R)
Regarding UNIT Roots:
forecast::ndiffs(x) gives me "1", so it should be safe that taking a first difference is ok
forecast::nsdiffs(x) gives "0"
A plot of the time series: plot(x)
after taking the first difference: plot(diff(x))
and finally a descomposition using stl(x)