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. enter image description here enter image description here

  • $\begingroup$ I don't see how you get an MA(3) out of the ACF. The first bar on the left = 1, as it's the 0-lag autocorrelation (don't ask me why), and the bar corresponding to lag 2 is pretty close to the square root of the bar corresponding to lag 1, so it looks like an AR(1) to me - as it also does from the PACF. $\endgroup$ – jbowman Jul 16 '18 at 17:04
  • $\begingroup$ Can you explain your PACF plot's x-axis? For instance there appears to be about 10 values before lag 2. How come? $\endgroup$ – Aksakal Jul 16 '18 at 17:14

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