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I have a problem to define the critical value of ACF and PACF which is a dashed lines in ACF and PACF plot in R. It looks the critical value has a constant value. Many sources said that The critical value will be different based on Lag. So which one is correct?

Please give me the certain answer.. if you do, please give me the References too. Thankyou in Advanced.

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  • $\begingroup$ In most areas defining a priori critical values is pointless, e.g. stats.stackexchange.com/questions/132536/… $\endgroup$
    – Tim
    Commented Dec 11, 2015 at 9:42
  • $\begingroup$ @Tim in my case, it's important $\endgroup$
    – Shieryn
    Commented Dec 11, 2015 at 9:42
  • $\begingroup$ If it has, than it is even more important that you would not choose some arbitrary value that is meaningless in your situation... $\endgroup$
    – Tim
    Commented Dec 11, 2015 at 9:43
  • $\begingroup$ Possible duplicate of How to determine the critical values of ACF? $\endgroup$
    – user81847
    Commented Dec 11, 2015 at 9:44

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If you want to check the null hypothesis that the data is a realisation of a strong white noise you can use the standard portmanteau tests like the Box-Pierce or Ljung-Box test.

If you want to find the critical value (ie the confidence interval) of an ACF you can use the Bartlett’s formula (see part : Statistical inference with correlograms )

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