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st: AW: Calculating dynamic confidence intervals after ARIMA


From   "Roland Geier" <mail@roland-geier.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: AW: Calculating dynamic confidence intervals after ARIMA
Date   Sun, 3 Jun 2012 11:19:58 +0200

Hi Carla,

maybe it's a fan chart you are looking for (aka "River of Blood" -
http://www.ecb.int/pub/mb/html/index.en.html)?
 If so, you might check out Chapter 14 of Stock/Watson, Introduction to
Econometrics 3rd ed., Pearson 2011, p. 582.

Such kind of charts are built of forecast intervals - these are like
confidence intervals except that they pertain to forecasts.
What you need are estimates of the RMSFE (root  mean squared forecast error)
which you can obtain from pseudo-out-of-sample(poos) forecasts (IMHO,
Stock/Watson p. 604 offers an excellent explanation).  "predict, mse"
calculates the mean squared errors of the observations, not of the forecasts
(pls correct me if I'm wrong) which can be used to get a confidence interval
for the model fit , but not to get dynamic, growing confidence intervals (as
you already pointed out).

I haven't found an out-of-the box module to calculate the poos forecasts.
With help of the description in Stock/Watson, the implementation is straight
forward.
The fan charts can be created with help of  overlapping rarea-graphics.

HtH

-- 
Roland



-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Hommes, Carla
Gesendet: Donnerstag, 3. Mai 2012 11:57
An: statalist@hsphsun2.harvard.edu
Betreff: st: Calculating dynamic confidence intervals after ARIMA

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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