Prediction or confidence intervals in proc x12?

[tatjana]

Does SAS produce prediction or forecast intervals in the forecast output of proc x12 ?

[udo_sas]

Hello -

Is this what you are looking for?

data sales;

   set sashelp.air;

   sales = air;

   date = intnx( 'month', '01sep78'd, _n_-1 );

   format date monyy.;

run;

proc x12 data=sales date=date;

   var sales;

   automdl;

   forecast lead=12;

   ods select forecastCL forecastsplot;

   ods output forecastCL=predicted;

run;

Thanks,

Udo

BTW: this book Practical Time Series Analysis Using SAS features plenty of nice illustrations including X12.

[tatjana]

Hi Udo,

thanks for your answer and the book link!

Unfortunately this statement only produces an output table with confidence limits which is called 'predicted'. What I am searching is an option to produce prediction limits instead of confidence limits.

Thanks a lot!

[tatjana]

Is there a way to calculate prediction intervals for ARIMA forecasts?

[udo_sas]

Hello -

The X12 procedure (like other procedures in SAS/ETS software) uses prediction standard errors to calculate confidence intervals for future predictions (the uncertainty grows with the forecast horizon).  Furthermore PROC X12 matches the Census Fortran Code - which you will find here: http://www.census.gov/srd/www/x12a/ - lots of details about the implementation can be accessed at this link.

Thanks,

Udo

[udo_sas]

Hello -

Some more information was shared by the X12 R&D team, which I'm adding to this thread for documentation purposes.

Thanks,

Udo

In the X-12-ARIMA Reference Manual, http://www.census.gov/ts/x12a/v03/x12adocV03.pdf and X-13ARIMA-SEATS Reference Manual,  http://www.census.gov/ts/x13as/docX13ASHTML.pdf section 4.7 Forecasting contains the same information:
“For a reasonably long time series, (Box and Jenkins 1976, pp. (267-269) observe that the contribution to forecast error of the error in estimating the AR and MA parameters is generally small, thus providing a justification for ignoring this source of error when computing the forecast standard errors.”
As I do not have the 1976 version of the Box and Jenkins book, I had to look for the equivalent in the 1994 version. In Chapter 9, Seasonal Models, Section 9.2.2, p. 334, I find “2. The forecasts are insensitive to small changes in parameter values such as are introduced by estimation errors.”

Chapter 9, Season Models is heavily cross-referenced with Chapter 5, Forecasting. After examining the X-12-ARIMA FORTRAN code, the standard error for the forecasts is computed as shown in 9.2.14 (5.1.16). This is just for the AR & MA error, the regression error effects are also considered in the computation. And the Ψ-weights are calculated as described in section 5.1. The Box-Jenkins reference was used for the computations apparently.

Is the customer actually getting different results? I believe that in this case, the problem is terminology. From http://robjhyndman.com/hyndsight/intervals/: “And I ask econometricians to stop being so sloppy about terminology.” The Census Bureau also uses the term “Confidence Interval”:

• Confidence intervals with coverage probability (0.95000)
• On the Original Scale

Although, Hyndman may find the terminology confusing, it does seem to be fairly standard practice.