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How do I interpret this autocorrelation and partial autocorrelation graph? ACF PCF

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The fact that almost all your autocorrelations are outside the Bartlett bands suggests you have substantial serial correlation in your model that you must account for.

The fact that the autocorrelations appear to exhibit damped oscillation, implies an autoregressive process AR(p) is a good starting guess.

The fact that the partial autocorrelations sharply cut off at 2, implies we can refine our guess to an AR(2) structure.

Returning to the fact that the autocorrelations oscillate, suggests that this series could have been produced by an AR(2) process with complex roots (a conjugate pair). In other words, if you write out the AR(2) model in generic form: enter image description here

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    $\begingroup$ with a hint of an ma12 . Only the data knows for sure ! If the OP posts his data I will put the data under my favorite microscope to detect sufficient structure to separate signal and noise ..... $\endgroup$
    – IrishStat
    Commented Dec 2, 2018 at 16:24
  • $\begingroup$ @IrishStat: Can you please expand on what hints of MA12? $\endgroup$ Commented Dec 2, 2018 at 16:38
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    $\begingroup$ the lag 2 and 14 are possibly suggestive of 12 (12+2=14). just a guess on my part after having studied/analyzed time series data for slightly over 50 years and having previously observed this phenomenon ( note mostly decaying 14,15,16,17,18 ) $\endgroup$
    – IrishStat
    Commented Dec 2, 2018 at 17:08

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