Problem Note 67629: PROC SSM might return incorrect results if one or more TREND statements are specified
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Certain model specifications in the SSM procedure can lead to incorrect results, including the model parameter estimates, fit statistics, smoothed and filtered component estimates, and other output generated by the procedure.
The results returned by PROC SSM might be incorrect if either of the following conditions is true:
- The model includes multiple TREND statements, or
- A combination of TREND and STATE statements are used in the model specification.
The results returned by PROC SSM are correct if either of the following conditions is true:
- No TREND statement is used in the model specification, or
- Only one TREND statement is specified and no STATE statements are used in the model specification.
An example of a specification that returns incorrect results is Example 6: Model with Multiple ARIMA Components in the PROC SSM documentation. The code used to specify the model is shown below. Note that two TREND statements are included in the model specification.
id date interval=month;
parm var1=0.016565 / lower=1.e-8;
trend airlineTrend(arma(d=1 sd=1 q=1 sq=1 s=12)) variance=var1;
trend ar2Noise(arma(p=2)) cross=(hwt) ar=0.600 0.246 variance=0.34488;
model logy = airlineTrend ar2Noise;
output outfor=For;
run;
The table below shows the expected results based on the Bell (2001) reference, along with the results currently returned by PROC SSM:
| Parameter | Reference | PROC SSM |
|---|---|---|
| MA_1 | 0.47 | 0.421 |
| SMA_1 | 0.42 | 0.31 |
| Var1 | 0.0052 | 0.004 |
Although these results might not appear to be vastly different, a check of the difference between the dependent variable, Logy, and the sum of the smoothed components for this model shows that the differences are too large. For the above model, this check can be performed as follows using the smoothed component estimates written to the OUTFOR= data set:
set for;
dif = logy - (smoothed_airlineTrend + smoothed_ar2Noise);
run;
proc means data=for min max;
var dif;
run;
For this model, the minimum and maximum DIF values are -0.0161 and 0.01372, respectively. The differences between the dependent variable and the sum of the underlying components should be on the order of 10e-8 or smaller.
This check can be difficult to perform for some model specifications, including models that contain regressors, dependent lags, or both. Technical Support can assist in defining this check for more complex models if needed.
For some models, the problem can be circumvented by replacing the component defined by a TREND statement with a comparable specification that involves the STATE and COMPONENT statements. This alternative specification can be difficult to program, depending on the trend type.
Click the Hot Fix tab in this note to access the hot fix for this issue.
Operating System and Release Information
| Product Family | Product | System | Product Release | SAS Release | ||
| Reported | Fixed* | Reported | Fixed* | |||
| SAS System | SAS/ETS | 64-bit Enabled AIX | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 |
| Windows 7 Ultimate x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Windows 7 Ultimate 32 bit | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Windows 7 Professional x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Windows 7 Professional 32 bit | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Windows 7 Home Premium x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Windows 7 Home Premium 32 bit | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Windows 7 Enterprise x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Windows 7 Enterprise 32 bit | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows Server 2012 Std | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows Server 2012 R2 Std | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows Server 2012 R2 Datacenter | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows Server 2012 Datacenter | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows Server 2008 for x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows Server 2008 R2 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows Server 2008 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows 10 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows 8.1 Pro x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows 8.1 Pro 32-bit | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows 8.1 Enterprise x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows 8.1 Enterprise 32-bit | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows 8 Pro x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows 8 Pro 32-bit | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows 8 Enterprise x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft Windows 8 Enterprise 32-bit | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Microsoft® Windows® for x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| z/OS 64-bit | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| z/OS | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| 64-bit Enabled Solaris | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| HP-UX IPF | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Linux for x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||
| Solaris for x64 | 14.1 | 15.3 | 9.4 TS1M3 | 9.4 TS1M8 | ||