Hope I'm able to find someone who can answer this question. The previous one didn't get answered!
Proc ucm is the SAS implementation (using state space concepts) to isolate the unobserved trend, seasonality & estimate the coefficients of regressors simultaneously.
Documentation/research on proc ucm is sparse. There are two questions I'm trying to find answers for: a. Does the dependent variable have to be treated for weak stationarity (differenced) before running proc UCM? Ans. http://www.iasri.res.in/sscnars/socialsci/17-Structural%20Time%20Series%20Models%20for%20Describing%20Trend%20in%20All%20India%20Sunflower%20Yield%20Using%20SAS.pdf
The attached paper seems to suggest that I don't need to worry about stationarity while using proc ucm.
However, I have found a contrary situation in my data. Consider my dependent is y. And, t & s are the smoothed trend & season components isolated by proc ucm. I'd have expected the series (y-t-s) to be stationary. But, it was not.
Thereby, I conclude that proc ucm is not capable of handling non-stationary time series, until I explicitly difference/stationarize the dependent.
Is this right?
b. I also have regressors which exhibit co-integrated relationships with y. From Granger's research paper, it is evident that spurious regression results when co-integrated series exists. But, I hear that's only if we use OLS-based proc reg. Proc UCM is based on maximum likelihood estimation. Is co-integration not a problem with maximum likelihood estimation based regression?
I could be ambiguous in my problem statement above and can clarify if need be.