Canonical correlations and canonical time series

In this paper, we revisit the problem of interrelations between large correlated data sets by considering cross correlations between a few linear combinations of the elements of each. This problem was studied by Hotelling (see Biometrika, vol.28, p.321-77) and Anderson (1958). We generalize the problem by studying linear transformations of the data sets, and applying our results to the case where one of the transformed data sets is noise corrupted. We derive best reduced-rank linear transformations and present asymptotic results. We conclude the paper by studying a causal filtering version of this problem and connecting it with the asymptotic case