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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.

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  • $\begingroup$ If you have the same firm(s) in multiple years there is panel structure you can use. If it is an actual time series, then you need some form of stationary to apply OLS. In any case auto correlation can be dealt with $\endgroup$ – Repmat Jan 13 '16 at 15:52
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Your question raises the topic of "Regression vs Box-Jenkins". This that might help you going forward as you pursue Transfer Function analysis https://onlinecourses.science.psu.edu/stat510/node/75 and ARIMAX model's exogenous components? . The relationship/differences between the analysis of cross-sectional data and time series data are discussed here http://www.autobox.com/cms/index.php/afs-university/intro-to-forecasting/doc_download/24-regression-vs-box-jenkins . By the way the "complications" are really "opportunities" as you sort out a possible useful model.

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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.

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  • $\begingroup$ You are right, Aksakal...tried to get a quick answer but why would i think there would be anything quick in statistical analysis:) Let me clarify this question and add to the post. $\endgroup$ – Wade Garrett Jan 13 '16 at 15:27
  • $\begingroup$ @WadeGarrett from your edit it's clear to me that you can't rely on pure stat or even econometrics literature. your question belongs to corporate finance field, there's a ton of papers doing similar analysis. you better browse that research. there are so many pitfalls in this sort of analysis, I don't know where to start. e.g. often you have to do pooled regression. $\endgroup$ – Aksakal Jan 13 '16 at 17:16
  • $\begingroup$ Thank you very much for the insight @Aksakal. I tend to agree...I think i'm having some trouble here as the hypothesis presented isn't clear enough. $\endgroup$ – Wade Garrett Jan 13 '16 at 19:53
  • $\begingroup$ @WadeGarrett, yes, you need to have a good hypothesis, of course. However, you'll also run into all sorts of endogeneity issues, e.g. aren't the measures of corporate structure dependent on profitability? $\endgroup$ – Aksakal Jan 13 '16 at 20:12

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