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Is there a way to utilize Canonical Correlation Analysis when your data are time series and repeated measures (i.e. your experimental units are not independent)? How might one approach the analysis of two sets of variables when the question is what relationships, if any, are there between one set of variables and the other. I was thinking canonical correlation analysis might help me do this, but my variables are count data (not normally distributed) taken over several consecutive years at the same location. In sum, one set of variables is the abundances of various species and the other set is the abundances of a variety of potential food resources.

Perhaps it's best to look at one dependent variable at a time instead of having several dependent variables. Any advice for a statistics novice?

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I don't think that using CCA will help you. It appears to me that you have a number of endogenous series ( abundance of species n in number ) and a number of exogenous series ( variety of food resources m in number ). I would suggest constructing n transfer functions each one optimized to fully utilize the information content in the m supporting series and their lags if appropriate while incorporating and unspecified stochastic structure with ARMA and unspecified deterministic structure like Level Shifts/Local Time Trends etc.. Having these n equations unser a "statistical microscope" might illuminate "commonalities" suggesting further grouping of the n equations into subsets.

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Thanks for your reply! I think you're right. My desire for using CCA comes mostly from the idea that I have two variable sets, and I want to see what relations, if any, exist between them. And my understanding is that CCA is often used for such purposes, but I have not come across any examples of CCA applied to time series data, like I have. I've also read multivariate normality is important for CCA, and my variables are most likely poisson distributed. I did a regularized CCA, all the canonical correlations came out as nearly 1, which I interpret to mean something is wrong. – Frank May 10 '11 at 21:10
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There are time-series uses for the canonical correlation, although the best one requires that you use a multiple-taper method of spectrum estimation. If all of your correlations are coming out as 1, that could be not that something is wrong, but that your series are highly correlated. This can happen easily if they are all seasonal and in-phase and you haven't prewhitened them. – Wesley Burr May 11 '11 at 1:00

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