Chaos Measure Dynamics and a Multifactor Model for Financial Markets

Abstract

Paper Length: 24 Pages
Suplementary Material: 88 Pages (mostly graphics)

This paper applies rolling windows to generate time-varying data series of selected chaos measures (i.e. Hurst exponent, maximum Lyapunov exponent, Lyapunov sum and sample entropy). The generated series are analysed to elaborate on time-varying data generating process (DGP) characteristics and the dynamic chaos (in-)stability of the original data. Furthermore, the denoted chaos measure series are combined with a macroeconomic indicator (i.e. the 10-year minus 2-year constant maturity curve) into several variations of a multifactor model based on the correlation structures to propose an explicative rationale for the price data set’s inherent factor composition and to bridge involved scientific fields (e.g. nonlinear dynamics or quantitative finance). The rolling windows are applied to cascadic (level 12) Haar-wavelet filtered (denoised) daily S&P500 logarithmic returns (2000-2020), which consist of a mixture between (hyperchaotic) deterministic and stochastic dynamics. The chaos measure series and the macroeconomic indicator are analysed by a nonlinear analysis framework, which allows the extraction of the characteristics of the empirical DGP of time-series. The chaos measure series each reveal own complex (non-chaotic) dynamics, differing from the underlying original data. Moreover, dynamical breaks or shifts (i.e. chaos instabilities) between conservative and dissipative system characteristics during (financial) crises periods can be stated. A combination of these chaos measure series in a multifactor model yields notable explicative power in terms of the composition of the price data, thus, stating a novel way of elucidating the underlying functioning of financial markets. Finally, the results are critically discussed, limitations shown and future avenues of research presented.

Keywords: time-varying chaos measures, multifactor financial model, financial markets, Lyapunov exponent, Hurst exponent, rolling window approach

JEL Classification: G1, C01, C02, C22, C18