Actually, I have read a pair of books about time series analysis, but I am still not sure about how to treat deterministic components, like trend and seasonality, in the exogenous variables in a time series model. Do I have to detrend and deseasonalize the covariates before I use them as axplanatory variables in a time series model? I would also be thankful for a reference.

Thank you in advance!


Unfortunately there are many possibilities.

1) Are seasonal factors stochastic or deterministic? 2) Does these seasonal factors affect both dependent and independent variables? 3) Do you have a system of simultaneous dynamic equations which has to be estimated jointly?

Following article by K. Wallis is interesting.


In most detailed level you have a multivariate input-output system with very complicated transfer function - polynomial matrix operator structure.

It seems that doing seasonal adjustment for the time-series separately leads at least to the inefficient estimates.



  • $\begingroup$ It seems that it is not a simple question. I am surprised that this Topic is not treated or explicitly treated in the books. $\endgroup$ – user2317915 Oct 16 '13 at 14:38

It may not be a good idea to consider trend & Seasonality as deterministic components of your dependent variable.

The Un-observed component model approach is an ideal way to handle such ambiguities. It estimates the trend, seasonality & other exogenous variables as well.

http://ideas.repec.org/h/eee/ecofch/1-07.html is your starting point.

  • $\begingroup$ Hey, it was not really about the inclusion of seasonal component to explain the response variable, but how to handle the seasonality in the regressors. $\endgroup$ – DatamineR Oct 15 '13 at 13:42
  • $\begingroup$ Yes, JohnnyB. Maybe I wasn't clear. PROC UCM helps estimate trend & seasonality components from your response variable pattern. You don't have to explicitly estimate the trend/seasonality using indicator variables/proc timeseries etc. support.sas.com/documentation/cdl/en/etsug/60372/HTML/default/… Hope I could explain better. $\endgroup$ – Learnerbeaver Oct 15 '13 at 14:20

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.