PHASE SYNCHRONIZATION ANALYSIS OF FINANCIAL TIME SERIES

Abstract

Research applying concepts and tools of nonlinear dynamics and statistical physics has been extended to the study of time series across multiple disciplines [12] [8]. Manifold-based dimensionality reduction methods have gained increasing attention for their usefulness at revealing the nonlinear degrees of freedom underlying large data structures with multiple subunits interacting nontrivially as a result of external stimuli [13][1]. The spawning emerging properties, whose geometry in the high-dimensional input space may be submersed to a lower dimensional manifold representation, express the low-dimensional local properties of the original time series data. Normally, market indices are composed of a nations largest stock exchanges, the S&P 500 is one such index.