Regression and Time Series I was posed a problem by a colleague that i am struggling with.  He is interested in the relationship between 10 variables and a single dependent, continuous variable.  This could simply be an OLS problem; however, he also wants to relate it to time.  He has a hypothesis that the relationship between the 10 variables and the dependent variable change over a 7 year period.  What model should I be looking into to help him answer his question?
[EDIT] 
The independent variables are measures of a company structure (board size, etc.) and the dependent is firm value (eg shareholder return).  By design these would have a level of autocorrelation I believe.  If it were cross-sectional (ie a single year) an OLS seems like the appropriate approach.  I am looking for the change in relationship over subsequent years.  To add a wrinkle we are also trying to control for firm size.
 A: You can do this with numerous parameter constancy tests, e.g. Chow test. The idea's to regress over two different periods and compare the parameters, whether they have changed substantially. "Structural break" is another key word for Googling.
You didn't give nearly enough information to help further. There are complications with time series as opposed to [cross-sectional] OLS regression, but it's a big topic. OLS might not be applicable at all in its simplest forms for time series data, it depends on the autocorrelations of variables of which you gave no information at all. So, my answer is the best you can get given the description you gave.
A: Your question raises the topic of "Regression vs Box-Jenkins". This that might help you going forward as you pursue Transfer Function analysis and ARIMAX model's exogenous components?. The relationship/differences between the analysis of cross-sectional data and time series data are discussed here. By the way the "complications" are really "opportunities" as you sort out a possible useful model.
