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I'm not sure how to interpret the autocorrelation pattern I'm seeing in this time series and any help would be very appreciated. Below is the ACF plot for my data. To me this looks like seasonal nonstationary but I'm a beginner so I can't be sure.

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The PACF is where I'm more confused. How should I interpret the declining correlation followed by the spike at lag 5? The literature I've read doesn't seem to help.

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Here are the ACF and PACF plots of the first differences: enter image description here

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  • $\begingroup$ Does the lag 5 have meaning for your data? Does your data have some similarity 5 measurements ago? Are you familiar with seasonality? $\endgroup$
    – user2974951
    Commented Aug 19, 2019 at 9:26
  • $\begingroup$ @user2974951 I am familiar with seasonality. I have no idea why the 5th lag would be so meaningful. Would this still be seasonality if the preceding lag isn't statistically significant? $\endgroup$
    – Michael Howell
    Commented Aug 19, 2019 at 22:43
  • $\begingroup$ It's hard to tell, it could be something, it could be nothing. From ACF and PACF you can conclude that your series is not stationary and that there may be some periodicity / seasonality. Try adding some AR or MA terms and see what happens. $\endgroup$
    – user2974951
    Commented Aug 20, 2019 at 5:58
  • $\begingroup$ @user2974951 Unit root test does conclude nonstationarity. If I try to minimize AIC I get an ARIMA (4,1,2). $\endgroup$
    – Michael Howell
    Commented Aug 20, 2019 at 22:13
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    $\begingroup$ In any case, if your selected model shows no more autocorrelation and seasonal terms do not help then you are done. $\endgroup$
    – user2974951
    Commented Aug 22, 2019 at 13:12

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