st: Calculating dynamic confidence intervals after ARIMA

["Hommes, Carla" <CHommes@diw-econ.de>]

Dear Statalisters,

after an ARIMA-X estimation I want to calculate and draw confidence intervals for my dynamic forecasts for several period ahead into the future.
Typically, these should look like funnel-shaped braces around the forecast.

My estimation command looks like this:
arima y x1 x2 x3, ar(1) ma(1)

The following solution (which I found on statalist, credit to Bob Yaffee) only produces parallel intervals around the forecast:
(seems to be valid only for the one-step-ahead forecast)

  Type: predict forecast
  then: predict fvar, mse
  Then: generate upper=forecast + 1.96*sqrt(fvar)
        generate lower=forecast - 1.96*sqrt(fvar)
  Then: tsline y forecast upper lower, title(My Forecast Profile)

What I'm looking for are dynamic, growing confidence intervals that in each period after the prediction starts take into account the uncertainty of the previous period's forecast of all components.

How can I do this in STATA?

Any help would be greatly appreciated!

Thanks
Carla

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