I am trying to do a forecasting exercise for a series, x. My forecast
model consists of the following

I first regress log(x) on time and dummy variables for each month.
lm(log(x) ~ time + monthly dummies)
I then use predict() to obtain a prediction for the next year.

I then fit an AR(6)/AR(12) model on the residuals of the regression.
I use predict() here also to obtain the prediction for the next year

My final forecast is the sum of the two predictions i.e. predict.lm
(from the regression, interval="prediction") and p$pred (from the AR
model). I then take the exp(of the sum) to plot it against my orginal
time series. (I assume that the Cov(x,y)=0 and therefore take the exp(sum)).

I now want to draw a confidence interval for my forecast. I realise that
I will have to add the standard errors from both the regression and the
AR() model to obtain the final standard error after which I will
calculate the confidence interval. I realise that I cannot just add the
two standard errors and take the exp() as in the case of the forecast.
My question is the following

Can someone help me to obtain the standard error for the final series?
How do I incorporate the SEs from the AR model? Or is there some other way I
can
calculate the confidence interval?

I know that if in predict.lm() I use interval="prediction", I get the
prediction interval for the yhat. However this is for the regression of
log(x) on time and monthly dummies. I can make an interval using p$pred
+-1.96*p$se from the AR model. Again this is for log(x). How can I use these
two to obtain the final interval for x as opposed to log(x)?

Thanks,

--
Renuka Sane

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