2
$\begingroup$

I have created a AR(2,1,0) model with the first two parameters equal to -1.08 and -0.33. I understand that a autoregressive parameter equal to 1 implies non-stationarity and a random walk process so I'm assuming the effect is the same if the parameter is a -1. So what does it mean when the parameter is greater than one? This model performs pretty well so I'm not sure if something is incorrect.

$\endgroup$
4
  • $\begingroup$ @Michael For an AR(1), the absolute value of the parameter being >1 implies nonstationarity. For an AR(2) it needn't. See stats.stackexchange.com/questions/118019/… (among a number of other posts) $\endgroup$
    – Glen_b
    Commented May 18, 2019 at 6:21
  • $\begingroup$ @Glen_b, Aksakal's answer and the linked thread suggests the opposite to your first sentence. What do you think about that? $\endgroup$ Commented May 20, 2019 at 11:13
  • $\begingroup$ I believed Aksakal to be discussing an ARIMA(1,1,0). $\endgroup$
    – Glen_b
    Commented May 21, 2019 at 3:10
  • $\begingroup$ Whoever closed this question, the link is irrelevant to this question. This question is about AR(2) process and the link is about AR(1) process and AR with coefficients -1.08 and -0.33 DO SATISFY the stationary condition for AR(2)! see stats.stackexchange.com/questions/118019/… $\endgroup$
    – KH Kim
    Commented Jan 29, 2023 at 4:20

1 Answer 1

1
$\begingroup$

No, autoregressive parameter greater than 1 in absolute value does not mean nonstationarity or random walk. It leads to explosive time series in most practical contexts. See, this question.

$\endgroup$
1
  • $\begingroup$ No, autoregressive parameter greater than 1 does not necessarily mean explosive time series for AR(2). see my comment above. $\endgroup$
    – KH Kim
    Commented Jan 31, 2023 at 17:22

Not the answer you're looking for? Browse other questions tagged or ask your own question.