Take the antilog of the log{y}=z transformed actual and fitted or forecast
values from the ARIMA model, which if in natural logs will  be EXP(z).

On Sat, 4 Jan 2025, 23:59 Cottrell, Allin, <cottr...@wfu.edu> wrote:

> On Sat, Jan 4, 2025 at 2:55 PM <dbrila...@yahoo.gr> wrote:
> >
> > Hi, I found that my data become stationary (after differentiate) the log
> data with best ARIMA(p,d,q)  How do I rebuilt the ARIMA forecast to the
> origina scale before log?
> > Tanks in advance
>
> There's a standard means of converting from a forecast or fitted value
> of log(y) to that of y itself, if the error term is reckoned to be
> normal, plus some variations on the theme. Dave Giles has quite a nice
> discussion of the point: see
> https://davegiles.blogspot.com/2014/12/s.html
>
> Allin Cottrell
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