I have a time series model from the package "Quandl" and I am trying to understand what the effects of differencing are on certain aspects of the model, primarily the PACF. In the plot of the times series and the decomposition after differencing the process once, it is easy to see that the trend is removed and the data is stationary (a KPSS test confirms this). The differences in the ACF are also quite easy to identify. I am having trouble understanding how differencing effected the PACF though. The image on the left is the differenced process, y_t, and the right is the original process, x_t. I can see that all of the PACF values have decreased, but I don't know how to interpret this. I have interpreted the differenced process to be AR(1) based on the PACF and MA(3) based on the ACF.