Correlation based on binary events I have a system with 5 components. Every 10 seconds the signal travels to all of them and I know how many of them responded. I need to know there there is a correlation in response. So, my time series data looks something like:
A    B    C    D    E
-----------------------
1    0    1    1    1
1    1    1    1    1
1    0    0    0    1
1    0    1    0    1
............

there are about 10,000 rows
Can I use a simple correlation function to see if there is correlation between occurrences of the above 5. Or is there a better way for this?
 A: Yes, you can compute the sample correlation matrix and see what the correlations are (in R this is as sample as cor(X) where X is your data matrix). But I'm not sure what you'll be able to conclude from these values; you'll need to define what you're looking for before you can properly test it.
For example, without any additional knowledge of what distribution your data comes from, one option would be to perform a $\chi^2$-test on each pair of columns to determine if they're independent. However, it's likely that independence is not really what you care about: with 10,000 rows, it's very likely that such a test will determine that two columns are not independent even if the relationship between them is quite weak.
Maybe you'd be better served by performing logistic regressions using each column to predict the others; the magnitude of the coefficients would then indicate how good a predictor each column is of every other. But it's hard to say what the best approach is without knowing more about your problem. A good place to start thinking about would be: if an oracle could tell you exactly what the relationships between your columns are, what would you do with the information?
