Is it always true that an AR(p) process with a white noise error will be covariance stationary?

  • $\begingroup$ No it is not always true. $\endgroup$
    – Andrew M
    Sep 15, 2018 at 23:42
  • $\begingroup$ But it is true whenever we have P roots inside the unit circle? $\endgroup$
    – 123
    Sep 15, 2018 at 23:45
  • $\begingroup$ Hi: If any of the roots of the AR(p) are outside the unit circle, then the AR(p) is not stationary in mean which means that it;s definitely not covariance stationary. $\endgroup$
    – mark leeds
    Sep 16, 2018 at 1:19
  • $\begingroup$ I should add that an AR(p) with all roots inside the unit circle is, by definition, covariance stationary because the covariance of $y_{t}$ and $y_{s}$ is only a function of $(t-s)$. $\endgroup$
    – mark leeds
    Sep 17, 2018 at 0:36
  • $\begingroup$ Yes, this is correct if we are only talking about stochastic trends but not if the process also has a deterministic trend. It could have all roots within the unit circle but if there is still a deterministic trend then the process would still not be covariance stationary. $\endgroup$
    – Andrew M
    Sep 20, 2018 at 9:05


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