How can I calculate the Confidence Limits around the sum of daily estimates using Proc ARIMA?

[Chrkoch93]

We are using Proc ARIMA to estimate daily mortality using daily time series data from the previous 4 years. There are daily trends that we would like to be captured in our model, which is why we prefer to use daily time series data instead of monthly.

Our issue is that we want to present our daily estimates as monthly estimates. Is there a method we could use to sum our daily estimates and calculate a 95% confidence limit around those aggregates? 

Here is the code used to produce our daily estimates:

proc arima data=filename;
identify var=COUNT (1,365) 
crosscorr=monday  
crosscorr=tuesday
crosscorr=wednesday
crosscorr=thursday
crosscorr=friday
crosscorr=saturday
crosscorr=sunday
nlag=1000 stationarity=(adf=100);
run;
estimate p=(1 2 7 30)(365) q=(1)(7)(30)(365) nostable maxiter=250 method=ml;
run; 
forecast alpha=0.05 lead=366 interval=Day id=DATE;
run;
quit;

Thank you

[Rick_SAS]

Since no one has responded with an analytical method, I suggest using a bootstrap to compute the CIs. For time series, here are some references 

- the stationary bootstrap

- the moving block bootstrap