12-01-2014 12:53 PM
I have a question about using proc autoreg with the "nlag" option specified for serial correlation correction. When there are significant AR terms included in the model from the "nlag" statement, there are two output parameter estimate tables, the first "Parameter Estimates" which includes the AR estimates, and then "Autoregressive parameters assumed given" table which does not include the AR terms -- I'm wondering which should be used for obtaining 1) the actual parameter estimates that one would want to use for forecasting of future values (for using the model in practice), and 2) which table has the correct p-values that should be referenced with regards to considering the real statistical significance of each variable to asses whether it should be retained in the model or not. I've been reading a bunch online, and have found some useful information and guidance, but I don't feel comfortable that I have a definitive answer here. I know that the "autoregressive parameters assumed given" table seems to match the parameter estimates output via the "outest=" option dataset, but I've read some material indicating that the "Full (conditional) model" is used for future predictions, which seems like it may suggest that I should be using the estimates from the first "Parameter Estimates" table inclusive of the AR times, but I may not be interperting this correctly (the material I am referencing is: http://support.sas.com/documentation/cdl/en/etsug/63348/HTML/default/viewer.htm#etsug_autoreg_sect00...
If anyone has any information on this, or could at least point in the direction of some more straight-forward reference material, I would really appreciate it.
12-04-2014 08:20 AM
12-04-2014 09:52 AM
I was able to track down an explanation from Wen in Tech support. I hope this helps clear up any confusion.
The output with Autoregressive parameters assumed given are obtained by setting the AR parameters fixed at the estimated values and estimate the regression parameters. This will lead to the same parameter estimates on the regression parameters but different standard errors. The difference in the standard errors computation is discussed at:
then click on Variance Estimates and Standard Errors.
Regarding 1, to compute predicted values, the parameter estimates in the two tables should be the same, so there should not be a difference which table to use for computing predicted values. They can just use the OUTEST = data set.
Regarding 2, it is essentially a question of which standard error is considered more ‘accurate’. The first table is obtained from joint estimation of AR and regression parameters, while the second table is obtained from estimating regression parameters with given AR parameters. As discussed in the above mentioned section of documentation, the two methods of computing standard errors are compared as follows which may be helpful to the customer:
Park and Mitchell (1980) investigated the small sample performance of the standard error estimates obtained from some of these methods. In particular, simulating an AR(1) model for the noise term, they found that the standard errors calculated using GLS with an estimated autoregressive parameter underestimated the true standard errors. These estimates of standard errors are the ones calculated by PROC AUTOREG with the Yule-Walker method.
The estimates of the standard errors calculated with the ULS or ML method take into account the joint estimation of the AR and the regression parameters and may give more accurate standard-error values than the YW method. At the same values of the autoregressive parameters, the ULS and ML standard errors will always be larger than those computed from Yule-Walker. However, simulations of the models used by Park and Mitchell (1980) suggest that the ULS and ML standard error estimates can also be underestimates. Caution is advised, especially when the estimated autocorrelation is high and the sample size is small.
I hope this helps. If there are additional questions, please let me know.
The simple interpretation, I believe, is that your forecasted values will be the same regardless of which set of estimates you use, however your SE's and therefore CI's will differ. To ensure that you are utilizing the correct SE's, and applying the SE's in the right way to the forecast, please use the technique discussed here. SAS/ETS(R) 13.2 User's Guide
Hope this helps. -Ken
12-09-2014 02:20 PM
Thank you ets_kps for your extremely useful response. However one thing -- I'm still have a really difficult time interpreting from that SAS discussion which SE's/P-Values are more accurate/correct..it seems very ambiguous. It appears there is no clear distinction between which is always better to use?