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This is more a question about definition. On Wikipedia, it mentions taking a unit root process (that happens to be I(1)) and making it stationary via differencing. However, it doesn't state if all unit root processes are I(1). Can I(2) or higher order processes by unit root as well?

Are all I(1) processes unit root and are all unit root processes I(1)?

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You can have more than one unit root. An I(2) process has 2 unit roots.

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  • $\begingroup$ Oh right, the second lagged term could have a coefficient of 1 as well. Is that generally the definition, I(1) is 1 unit root, I(2) is two unit roots, etc... $\endgroup$
    – confused
    Commented Jul 28, 2020 at 19:38
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    $\begingroup$ For an I(d) process d shows how many times you have to be differenced to be stationary assuming you have a unit root(s). I am not sure either of our, essentially the same, comments are the definition of integration :) $\endgroup$
    – user54285
    Commented Jul 28, 2020 at 19:43
  • $\begingroup$ while it theory you can have a large number of unit roots in practice seasonal and non-seasonal units roots are rarely beyond 2 seems to be the consensus in the social sciences. $\endgroup$
    – user54285
    Commented Sep 20, 2021 at 0:09

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