Chaoticity Versus Stochasticity in Financial Markets: Are Daily S&P 500 Return Dynamics Chaotic?
- In this study, we empirically show the dynamics of daily wavelet-filtered (denoised) S&P 500 returns (2000–2020) to consist of an almost equally divided combination of stochastic and deterministic chaos, rendering the series unpredictable after expiration of the Lyapunov time, resulting in futile forecasting attempts. We achieve a clear distinction of the true nature of the underlying time series dynamics by applying a novel and combinatory chaos analysis framework comparing the wavelet-filtered S&P 500 returns with respective surrogate datasets, Brownian motion returns and a Lorenz system realisation. Furthermore, we are the first to show the strange attractor of especially the daily-frequented S&P 500 return system graphically via Takens´ embedding and by spectral embedding in combination with Laplacian Eigenmaps. Finally, we critically discuss implications and future prospects in terms of financial forecasting.