Below are the ACF and PACF of a non-stationary time series.
Notice the slow linear decay and a partial autocorrelation lag 1 almost equal to one. These are indications of a non-stationary series where there is a unit root (i.e. the series can be made stationary by differencing).
Below are the ACF and the PACF of the differenced data. What is the most likely model for the original data set? (Hint: don't forget to include the differencing).
MA(1)
AR(1)
ARIMA(5,1,0)
ARIMA(0,1,1)