  Neural data analysis has increasingly incorporated causal information to
study circuit connectivity. Dimensional reduction forms the basis of most
analyses of large multivariate time series. Here, we present a new,
multitaper-based decomposition for stochastic, multivariate time series that
acts on the covariance of the time series at all lags, $C(\tau)$, as opposed to
standard methods that decompose the time series, $\mathbf{X}(t)$, using only
information at zero-lag. In both simulated and neural imaging examples, we
demonstrate that methods that neglect the full causal structure may be
discarding important dynamical information in a time series.
