Chaos measure dynamics in a multifactor model for financial market predictions

Abstract

To answer the question if chaos changes over time, we apply rolling windows to wavelet-denoised logarithmic S&P500 returns (2000–2020) and calculate consecutive chaos measures (e.g., Hurst-, maximum Lyapunov exponent or sample entropy). We state time-variation of the chaos measure series, indicating chaos instability or inherent chaotic time variations of the underlying (hyper-)chaotic deterministic S&P500 return system. Moreover, we intend to deploy these chaos measure series as predictors for the denoted financial series. An optimised selection of these series is applied as input features for a dynamic factor model realised as deep learning multilayer perception neural network to predict the original S&P500 price and return series out-of-sample. The approach is validated by performance metrics (e.g., explained variance score) and the residuals are shown to be non-autocorrelated and ∼iid. Finally, we compare the results with selected base or benchmark models (e.g., autoregressive models). Thus, the approach provides a novel multifactor model for practical market price predictions from a dynamical (inherent) system-based view.