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Can anyone reference an algorithm or paper which can help me convert a general SARMA model to an infinite AR polynomial in backshift operator B? I would like to do this in R somehow.

$$ \frac{\theta(B)\Theta(B^s)}{\phi(B)\Phi(B^s)} = 1 - \pi_1B - \pi_2B^2 - ... $$

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  • $\begingroup$ This may be of limited value if the sample size is less than the order of the "infinite polynomial" . $\endgroup$
    – IrishStat
    Commented Feb 7, 2020 at 12:08
  • $\begingroup$ Yeah I was hoping to find an algorithm where I could stop calculating $\pi$ weights at any point I choose. $\endgroup$
    – Frank
    Commented Feb 7, 2020 at 15:06
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    $\begingroup$ Polynomial arithmetic is what AUTOBOX implements to do this ... also make sure to include differencing operators $\endgroup$
    – IrishStat
    Commented Feb 7, 2020 at 15:11
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    $\begingroup$ In principle, a SARMA process is just an ARMA process with coefficient restrictions - so you can find the AR representation through matching coefficients, as for example explained here: stats.stackexchange.com/questions/171698/… $\endgroup$ Commented Feb 10, 2020 at 9:13

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