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If I used arima(data, c(1,0,1)) in R software and get this result:

R Output

How should I write the equation for $ARMA(1,1)$ or $ARIMA(1,0,1)$? Is the following correct?

$$ y_t=18.7083+0.8672y_{t-1}+0.4752\epsilon_{t-1}+\epsilon_t $$

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    $\begingroup$ Regarding the interpretation of the intercept (18.7083), you have likely got it wrong. See stat.pitt.edu/stoffer/tsa2/Rissues.htm. I also think the sign of MA should be inverted. $\endgroup$
    – Richard Hardy
    Commented Dec 7, 2022 at 13:29
  • $\begingroup$ So, from the reference and from what you said $y_t=2.4826+0.8673y_{t-1}-0.4752\epsilon_{t-1}+\epsilon_t$. Will this be correct? $\endgroup$
    – RRMT
    Commented Dec 7, 2022 at 13:56
  • $\begingroup$ How did you arrive at 2.4826? $\endgroup$
    – Richard Hardy
    Commented Dec 7, 2022 at 14:37
  • $\begingroup$ $18.7083(1-0.8673)=2.4826$ That is based on the page you linked. $\endgroup$
    – RRMT
    Commented Dec 7, 2022 at 23:32
  • $\begingroup$ I suppose it is OK then. And if so, you could write an answer to your own question. $\endgroup$
    – Richard Hardy
    Commented Dec 8, 2022 at 7:34

1 Answer 1

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Based on what Richard Hardy pointed out, the fitted $ARIMA(1,0,1)$ can be written as $$ y_t=2.4826+0.8673y_{t-1}-0.4752\epsilon_{t-1}+\epsilon_t $$ is the correct answer.

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