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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.

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    $\begingroup$ You don't need to treat stationarity before fitting a structural time series model or UCM. But you have to choose a model that is able to deal with the features observed in the data (seasonality, trends,...). If the residuals are not stationary, some components may need to be added to the model, e.g. a slope or a seasonal component. If you could post the data or at least the graphic of the data and autocorrelations of the residuals you may get more answers. Also, you say that you are using an UCM model but not the particular model: local level, basic structural model, trend plus cycle,... $\endgroup$ – javlacalle Dec 12 '14 at 11:55
  • $\begingroup$ Dealing with cointegration is not a matter of choosing an estimator, OLS, ML or other. If there is a cointegration relationship between the variables, then it may be better to work with a multivariate model. $\endgroup$ – javlacalle Dec 12 '14 at 11:56
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Depends if you have missing data in the series, from SAS : This example shows how you can use the UCM procedure for ARIMA modeling. The parameter estimates and predictions for ARIMA models obtained by using PROC UCM will be close to those obtained by using PROC ARIMA (in the presence of the ML option in its ESTIMATE statement) if the model is stationary or if the model is nonstationary and there are no missing values in the data. See Chapter 7, The ARIMA Procedure, for additional details about the ARIMA procedure. However, if there are missing values in the data and the model is nonstationary, then the UCM and ARIMA procedures can produce significantly different parameter estimates and predictions. An article by Kohn and Ansley (1986) suggests a statistically sound method of estimation, prediction, and interpolation for nonstationary ARIMA models with missing data.

http://support.sas.com/documentation/cdl/en/etsug/60372/HTML/default/viewer.htm#etsug_ucm_sect047.htm

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