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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.

Michael Howell
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  • @Michael For an AR(1), the absolute value of the parameter being >1 implies nonstationarity. For an AR(2) it needn't. See https://stats.stackexchange.com/questions/118019/a-proof-for-the-stationarity-of-an-ar2 (among a number of other posts) – Glen_b May 18 '19 at 06:21
  • @Glen_b, Aksakal's answer and the linked thread suggests the opposite to your first sentence. What do you think about that? – Richard Hardy May 20 '19 at 11:13
  • I believed Aksakal to be discussing an ARIMA(1,1,0). – Glen_b May 21 '19 at 03:10
  • 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 https://stats.stackexchange.com/questions/118019/a-proof-for-the-stationarity-of-an-ar2?noredirect=1&lq=1 – KH Kim Jan 29 '23 at 04:20

1 Answers1

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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.

Aksakal
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  • No, autoregressive parameter greater than 1 does not necessarily mean explosive time series for AR(2). see my comment above. – KH Kim Jan 31 '23 at 17:22