# A simple yet confusing ARIMA

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

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

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

• 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. Commented Dec 7, 2022 at 13:29
• 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?
– RRMT
Commented Dec 7, 2022 at 13:56
• How did you arrive at 2.4826? Commented Dec 7, 2022 at 14:37
• $18.7083(1-0.8673)=2.4826$ That is based on the page you linked.
– RRMT
Commented Dec 7, 2022 at 23:32
• I suppose it is OK then. And if so, you could write an answer to your own question. Commented Dec 8, 2022 at 7:34

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.