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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.

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

Richard Hardy
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Frank
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  • This may be of limited value if the sample size is less than the order of the "infinite polynomial" . – IrishStat Feb 07 '20 at 12:08
  • Yeah I was hoping to find an algorithm where I could stop calculating $\pi$ weights at any point I choose. – Frank Feb 07 '20 at 15:06
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    Polynomial arithmetic is what AUTOBOX implements to do this ... also make sure to include differencing operators – IrishStat Feb 07 '20 at 15:11
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    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: https://stats.stackexchange.com/questions/171698/how-to-calculate-impulse-responses-for-a-given-autoregressive-process/171709#171709 – Christoph Hanck Feb 10 '20 at 09:13

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