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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