  The Dynamic Mode Decomposition (DMD) extracted dynamic modes are the
non-orthogonal eigenvectors of the matrix that best approximates the one-step
temporal evolution of the multivariate samples. In the context of dynamical
system analysis, the extracted dynamic modes are a generalization of global
stability modes. We apply DMD to a data matrix whose rows are linearly
independent, additive mixtures of latent time series. We show that when the
latent time series are uncorrelated at a lag of one time-step then, in the
large sample limit, the recovered dynamic modes will approximate, up to a
column-wise normalization, the columns of the mixing matrix. Thus, DMD is a
time series blind source separation algorithm in disguise, but is different
from closely related second order algorithms such as the Second-Order Blind
Identification (SOBI) method and the Algorithm for Multiple Unknown Signals
Extraction (AMUSE). All can unmix mixed stationary, ergodic Gaussian time
series in a way that kurtosis-based Independent Components Analysis (ICA)
fundamentally cannot. We use our insights on single lag DMD to develop a
higher-lag extension, analyze the finite sample performance with and without
randomly missing data, and identify settings where the higher lag variant can
outperform the conventional single lag variant. We validate our results with
numerical simulations, and highlight how DMD can be used in change point
detection.
