I'm trying to understand the meaning of cut off and tails off in time series plot of ACF and PACF.enter image description here

What "Cut off after lag" mean? This about limit?

What "Tails off" mean?

In the example above, the book that I'm using to study, say that is an AR process.

enter image description here

But I can't figure out the meanings of "cuts off" and "tails off"


1 Answer 1


"Cuts off" means that it becomes zero abruptly, and "tails off" means that it decays to zero asymptotically (usually exponentially).

In your picture, the PACF "cuts off" after the 2nd lag, while the ACF "tails off" to zero. You probably have something like an AR(2).

  • 3
    $\begingroup$ If and only if ... there are no pulses , level shifts , time trends , seasonal pulses and the model is invariant over time and the error process is invariant over time otherwise interpreting the acf and pacf is at best problematic..and help is needed in terms of (gasp !) heuristics, $\endgroup$
    – IrishStat
    Oct 25, 2016 at 20:29
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    $\begingroup$ I interpreted the question to be about ARMA processes only, so all of your stated requirements above are trivially satisfied. The fact that the ACF/PACF may be misleading when selecting an ARMA model for real-world data is true, but a different question. $\endgroup$
    – Chris Haug
    Oct 25, 2016 at 21:19
  • 4
    $\begingroup$ We are in agreement .. apologies for over-reading your remarks but I intended the comment as a gentle warning to.newbies in time series analysis who are swayed by auto.arima and the like as they attempt to fit ARIMA models without concern for the points I raised... $\endgroup$
    – IrishStat
    Oct 25, 2016 at 22:07

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