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.

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

  • $\begingroup$ 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
  • 1
    $\begingroup$ 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
  • 1
    $\begingroup$ 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


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.