On Wed, 17 Jul 2019, Yusuf Abduwahab Hassan wrote:

> Good morning all,
> Please how can i re-transform the  forecasts of the estimations in
> log-transformed data back to levels form?

Assuming that

- you want to forecast vie conditional expectation (ie with quadratic loss)
- your data are at least approximately normal

you can compute the expectation of the exponential as

E(exp(x)) = exp(E(x) + 0.5*v(x))

An example script with out-of-sample forecast on the famous Box-Jenkins
"airline" dataset follows

<hansl>
open bjg.gdt --quiet

series insample = t < "1960:3"
series f = NA
smpl insample == 1 --restrict
arima 0 1 1 ; 0 1 1 ; lg
fcast --out-of-sample

matrix F = $fcast + 0.5 * $fcse.^2
smpl insample == 0 --restrict --replace
f = exp(F)
setinfo f --graph-name="forecast"
smpl full

gnuplot g f --time-series --with-lines --output=display
</hansl>

Hope this helps.


-------------------------------------------------------
   Riccardo (Jack) Lucchetti
   Dipartimento di Scienze Economiche e Sociali (DiSES)

   Università Politecnica delle Marche
   (formerly known as Università di Ancona)

   r.lucchetti@univpm.it
   http://www2.econ.univpm.it/servizi/hpp/lucchetti
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