THE FINITE SAMPLE PERFORMANCE OF DYNAMIC MODE DECOMPOSITION

Abstract

We analyze the Dynamic Mode Decomposition (DMD) algorithm as applied to multivariate time-series data. Our analysis reveals the critical role played by the lag-one cross-correlation, or cross-covariance, terms. We show that when the rows of the multivariate time series matrix can be modeled as linear combinations of lag-one uncorrelated latent time series that have a non-zero lag-one autocorrelation, then in the large sample limit, DMD perfectly recovers, up to a column-wise scaling, the mixing matrix, and thus the latent time series. We validate our findings with numerical simulations, and demonstrate how DMD can be used to unmix mixed audio signals.