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Hey, I didn't know that ARIMA models could do that

You were taught and told through books, teachers, websites and your software that your AR model coefficient can't be outside the -1 to +1 region. This is also often stated as that "unit root" needs to be outside the unit circle, but this just isn't true. A criticism of Box-Jenkins modeling was that it wasn't applicable to growth models.  See here for more.  http://www.autobox.com/cms/index.php/blog

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