  We demonstrate the application of an algorithmic trading strategy based upon
the recently developed dynamic mode decomposition (DMD) on portfolios of
financial data. The method is capable of characterizing complex dynamical
systems, in this case financial market dynamics, in an equation-free manner by
decomposing the state of the system into low-rank terms whose temporal
coefficients in time are known. By extracting key temporal coherent structures
(portfolios) in its sampling window, it provides a regression to a best fit
linear dynamical system, allowing for a predictive assessment of the market
dynamics and informing an investment strategy. The data-driven analytics
capitalizes on stock market patterns, either real or perceived, to inform
buy/sell/hold investment decisions. Critical to the method is an associated
learning algorithm that optimizes the sampling and prediction windows of the
algorithm by discovering trading hot-spots. The underlying mathematical
structure of the algorithms is rooted in methods from nonlinear dynamical
systems and shows that the decomposition is an effective mathematical tool for
data-driven discovery of market patterns.
