# Deterministic components in covariates/exogenous variables in time series models

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!

## 2 Answers

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.

http://www.nber.org/chapters/c3905.pdf

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.

Regards,

-A

• It seems that it is not a simple question. I am surprised that this Topic is not treated or explicitly treated in the books. – 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.

• 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. – DatamineR Oct 15 '13 at 13:42
• 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. – Learnerbeaver Oct 15 '13 at 14:20