I'm trying to estimate the standard error of the intercept in ARIMAX(1,0,2) model using R.

Since the reported 'intercept' in regression output is actually some kind of mean value I applied this formula to get the 'real' intercept:

Constant = Mean*(1-AR coefficient)

The problem is that I'm not sure how to calculate the standard error of this constant. I was thinking to use propagation of uncertainty. Does anyone know how the error propagation formula would look like in this case? Or if there is any other way to calculate the standard error of the constant in ARIMAX model?

Any help would be greatly appreciated.

  • $\begingroup$ Hi Justina, welcome to CV! On this site there's no need to say "thank you" or "Any help would be appreciated" at the end of your post - it might seem rude at first, but it's part of the philosophy of this site (tour) to "Ask questions, get answers, no distractions" and it means future readers of your question don't need to read through the pleasantries. $\endgroup$ Commented May 14, 2018 at 15:13

1 Answer 1


There is no need to investigate error propogation . Simply multiply the reported standard error of the mean by the factor 1-AR ...since the constant and the mean are proportional .

  • 1
    $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review $\endgroup$ Commented May 14, 2018 at 16:25
  • $\begingroup$ i expanded on my answer to the question $\endgroup$
    – IrishStat
    Commented May 14, 2018 at 18:54

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