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Prediction or confidence intervals in proc x12?

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New Contributor
Posts: 3

Prediction or confidence intervals in proc x12?

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

SAS Employee
Posts: 416

Re: Prediction or confidence intervals in proc x12?

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.

New Contributor
Posts: 3

Re: Prediction or confidence intervals in proc x12?

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!

New Contributor
Posts: 3

Re: Prediction or confidence intervals in proc x12?

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

SAS Employee
Posts: 416

Re: Prediction or confidence intervals in proc x12?

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

SAS Employee
Posts: 416

Re: Prediction or confidence intervals in proc x12?

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.

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