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I have the following ACF and PACF plots for a time series. I'm very new to time series so I might be interpreting this wrong, but it seems like the ACF is indicating an MA(1) process because it tails off after lag 1 but the PACF looks more like an MA(3) based on the 95% CI lines. Am I interpreting one or both of these plots incorrectly? enter image description here enter image description here

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    $\begingroup$ You're interpreting the PACF incorrectly. The PACF gives you information about the AR structure, not the MA structure. If you were going by the PACF alone, it would suggest an AR(4) model, perhaps. $\endgroup$ – The Laconic Aug 10 '18 at 22:30
  • $\begingroup$ Yep, you're misreading the PACF. They look consistent to me $\endgroup$ – Glen_b Aug 10 '18 at 23:19
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ACF gives you information about moving average(MA) processes while PACF gives you insight about auto regressive (AR) processes. The graphs you have in your output can produce a consistent model. For a brief explanation (without the theory), you can look at Table 3.1 p 104 here. For more theoretic answer you can read couple of sections before the graph.

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