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Lets start out by saying that I'm a novice with statistics.

I'm looking to analyze the relationship between Return on Sales (ROS) and Asset Turnover (TAT) over time to see how they impact firm profitability (Return on Assets (ROA)).

I have a few ways to look at this data.

First, I can look at the entire economy in the US as one giant company and compute the variables for each year of the time series. What would be the proper test to say that the relationship between these two variables changes over time? A test for cointegration to say that the relationship is non-stationary?

Second, I can look at each company on a yearly basis and evaluate the relationship between the two variables in that way. My concern would be that there are massive outliers in the data set so a weighted regression would need to be used. Given that I would have >4,000 samples (distinct companies) for each year is there an appropriate test to look at this data and possibly say something meaningful about the relationship of the two variables? My other thought was possibly using something like the Chow test.

If this is too vague let me know and I'll see if I can be more clear!

Thanks

rwdvc
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First, I am not sure how large is the time period. If you have less than 15 years, it is better avoid using cointegration. Second, since you are saying that you have 4000 samples each year, I am assuming that you have panel data. Again, if you have time less than 15 years you can avoid using panel cointegration. You can try using fixed effects, random effects, and pooled OLS model. There is Hausman test and other tests that will help you decide why you want to choose one over other. Please have a look at the Introductory Econometrics book by Wooldridge for introduction on panel data. If your time is larger than 15 years, you can think of structural break in data and there are large number of tests to decide on those for both time series and panel data.

Nick Cox
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Metrics
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  • So I'll have between 23 and 45 years of data for each country. The 4,000 samples, pardon my previously incorrect wording, would actually be 4,000 different companies in each year time period. For example the ROS & TAT for each company within the S&P 500. I appreciate your input and I'll check out the recommended book! – rwdvc Jul 11 '13 at 00:46
  • Great; In that case you can use panel cointegration test, but it ultimately rests upon whether it is common in your area. But, you can always proceed with fixed effect. – Metrics Jul 11 '13 at 01:09