What is the meaning of an autoregressive parameter greater than one? [duplicate]

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 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) Commented May 18, 2019 at 6:21
• I believed Aksakal to be discussing an ARIMA(1,1,0). Commented May 21, 2019 at 3:10
• 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 stats.stackexchange.com/questions/118019/… Commented Jan 29, 2023 at 4:20

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.

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