How can I calculate covariance of quasi-Poisson-distributed variables in R? I have two time series of count data which I believe are correlated.  Is there an equivalent to cov() that assumes an overdispersed Poisson rather than a normal distribution?  If there is a significance test for this (noting that both series increase over time but that doesn't prove correlation), so much the better.  I wondered if vcov() might help but it focuses on parameters of a solved model.  More broadly, I'm looking for a measure of the similarity between two variables which is appropriate for quasi-Poisson data.
 A: The cov() function in R just calculates the empirical correlation, there is no assumption about normality in that.  Of course, if you go longer, like doing inference about the correlation, you need a model, and normality might simplify the analysis.  Or you could just bootstrap!
I think you should really edit the question to give more information about the situation giving rise to your data so that we could think about how to model it.  That's the way to go about to find a more meaningful measure than simply the correlation coefficient. Did you make a simple scatterplot of your two time-series?
Some more thoughts. If the counts are varying wildly, maybe indicating that the underlying mean is nonconstant (you say both series are increasing in trend, suggesting that), one idea is to apply a variance-stabilizing transformation, which in poisson and quasi-poisson case is just the square-root.  After that you can apply methods for  normally-distributed time series, at least as an approximation. 
