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.
Here goes:
In my field (developmental science) we apply DFA to intensive multivariate time-series data for an individual. Intensive small samples are key. DFA allows us to examine both the structure and time-lagged relationships of latent factors. Model parameters are constant across time, so stationary time-series (i.e., probability distributions of stationarity of stochastic process is constant) is really what you are looking at with these models. However, researchers have relaxed this a bit by including time-varying covariates. There are many ways to estimate the DFA, most of which involve the Toeplitz matrices: maximum likelihood (ML) estimation with block Toeplitz matrices (Molenaar, 1985), generalized least squares estimation with block Toeplitz matrices (Molenaar & Nesselroade, 1998), ordinary least squares estimation with lagged correlation matrices (Browne & Zhang, 2007), raw data ML estimation with the Kalman filter (Engle & Watson, 1981; Hamaker, Dolan, & Molenaar, 2005), and the Bayesian approach (Z. Zhang, Hamaker, & Nesselroade, 2008).
In my field DFA has become an essential tool in modeling nomothetic relations at a latent level, while also capturing idiosyncratic features of the manifest indicators: the idiographic filter.
The P-technique was a precursor to DFA, so you might want to check that out, as well as what came after... state-space models.
Read any of the references in the list for estimation procedures for nice overviews.
Best Answer
Ideas for factor analysis and PCA:
Canonical correlation analysis
CCA
orcancor
takes correlation matrices as input.sem
can take a correlation matrix as input.