Multiresolution Analysis of the US Stock Market Nonlinear Dynamics Based on Surrogate Data and Singular Value Decomposition

An accurate characterization of the nonlinear behavior of stock markets is of prime importance for the proper design of investment portfolios and the pricing of financial instruments. Surrogate data analysis based on phase randomization and singular value decomposition (SVD) was used to test for multiresolution nonlinear dynamics in the US stock market. The study pointed to the presence of nonlinear dynamics acting at different time scales. Nonlinearity is stronger for larger time horizons and is directly linked to the diversity of patterns, quantified in terms of the SVD entropy, displayed by returns.