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Does $ARMA(p,q)$ process need to be invertible and have a causal stationary solution to be written in $MA(\infty)$ representation?

And if you write the process in terms of $Z_t$ instead of $X_t$, then you get $AR(\infty)$ form right?

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    $\begingroup$ What is the relationship between $Z_t$ and $X_t$? $\endgroup$
    – jbowman
    Apr 19, 2023 at 19:28
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    $\begingroup$ @jbowman That sounds like a good educated guess. It would be nice to know without having to guess ;-). $\endgroup$
    – whuber
    Apr 19, 2023 at 19:37
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    $\begingroup$ @whuber - yes, it would! $\endgroup$
    – jbowman
    Apr 19, 2023 at 21:10
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    $\begingroup$ @whuber sorry about that, i meant the roots being outside the unit circle for invertibility. $\endgroup$
    – eddie
    Apr 19, 2023 at 21:12
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    $\begingroup$ I'm afraid that doesn't explain anything at all about the relationship between $X_t$ and $Z_t$, or, for that matter, what they are. $\endgroup$
    – jbowman
    Apr 19, 2023 at 21:31

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