I'm having a bit of trouble understanding the blue dotted lines in the following picture of autocorrelation function: enter image description here

Could someone give me a simple explanation, what they are telling me?


The lines give the values beyond which the autocorrelations are (statistically) significantly different from zero. Your ACF seems to indicate seasonality. I recommend Forecasting: Principles and Practice by Hyndman & Athanasopoulos, which is freely available online. (You can also buy a paper version.)

  • $\begingroup$ What is the title of the book? The link is broken. $\endgroup$ – Konstantinos May 23 '17 at 17:39
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    $\begingroup$ @pidosaurus: good point, I should have noted the actual title of the book. I have edited my answer to include it. The entire otexts.com website seems to be down. Please just check back later - the book was online just a day ago, and I know the authors are working on the 2nd edition, so I'm sure it will come back - and the book is truly highly recommended. $\endgroup$ – Stephan Kolassa May 23 '17 at 18:09
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    $\begingroup$ Link works after a small edit: otexts.org/fpp . The book is well known/written and spectacular. Thank you. $\endgroup$ – Konstantinos May 23 '17 at 18:41
  • $\begingroup$ @pidosaurus: thanks for catching & editing that! Seems like I made an error in typing in the URL. (Makes me wonder how I got six upvotes before someone noticed...) $\endgroup$ – Stephan Kolassa May 23 '17 at 20:59
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    $\begingroup$ See this question for details on how the confidence band is actually calculated. $\endgroup$ – Candamir Nov 17 '17 at 21:33

It looks like seasonality (of length 18 periods) and a longer cyclical term of about 6 seasonal intervals.

It might also be caused by an actual periodic function

What does the PACF or IACF look like?

Edit: The plot looks to be one generated in R; the blue dashed lines represent an approximate confidence interval for what is produced by white noise, by default a 95% interval

  • $\begingroup$ I took the picture from a book and there isn't PACF given...but I'm only interested on the blue dotted line :) Thank you $\endgroup$ – jjepsuomi Feb 8 '13 at 11:43
  • $\begingroup$ Sorry, I got so caught up I forgot to answer that part. I have updated my answer. $\endgroup$ – Glen_b Feb 8 '13 at 12:40
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    $\begingroup$ You can get (a little) more information from the help for the function plot.acf under the entries for things with ci in their name under Arguments, as well as the whole of the Note section - find that help page here $\endgroup$ – Glen_b Feb 8 '13 at 22:41

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