Dear List,



I am looking to reveal the combination of environmental factors that bets
explain the observed variance in a uni-variate time series of a population.



I have approached this using two methods, and have different results,
therefore i was hoping somebody may have done something similar, or have
knowledge of the area, such that they could advise me of the best approach.



My first approach was to use canonical correlations i.e. search for
significant correlations between explanatory variables x1, x2 and x3  and
the time series,  this made sense to me and produced perfectly plausible  (
in line with a priori hypothesise) results. However, this approach  doesn't
take into account the other variables present.



To address this i then used a dynamic factor analysis - explaining temporal
variation in a set of n observed time series using linear combinations of a
set of m hidden random walks, where m << n. I then used  a AIC framework to
arrive at the most likely model.



http://cran.r-project.org/web/packages/MARSS/vignettes/UserGuide.pdf



However, the results differed, the variables present in the “best” AIC
model were not necessarily the ones with the strongest canonical
correlation.



Why my this be the case? Is there a better way to go about this?



Thanks

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