Why does an AR(p) process require the largest eigenroot to be <1/ characteristic roots lie outsied the unit circle to be stationary?

Asked Apr 09 '19 at 09:50

Active Apr 09 '19 at 16:59

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For reference, this is the paragraph in Wikipedia I'm struggling with.

https://en.wikipedia.org/wiki/Autoregressive_model

I do understand the simpler proof for under which conditions an AR(1) process is stationary, however I do not understand a.) how to make the connection between the condition for AR(1) to be stationary () and the generalized condition for the root |z| > 1.

b.) How to show that |z|>1 must hold for AR(p) to be stationary and the "intuition" behind the second condition (if there is any)

Any help is greatly appreciated. Thank you all in advance!

edited Apr 09 '19 at 16:59

Richard Hardy

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asked Apr 09 '19 at 09:50

Ella.H

Some intuition is provided at https://stats.stackexchange.com/questions/29121/intuitive-explanation-of-unit-root/29129#29129. – whuber Apr 09 '19 at 13:42
Thank you. The link is great for some basic intuition! – Ella.H Apr 11 '19 at 11:23

Why does an AR(p) process require the largest eigenroot to be <1/ characteristic roots lie outsied the unit circle to be stationary?

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