Chaoticity Versus Stochasticity in Financial Markets: Are Daily S&P 500 Return Dynamics Chaotic?

In this study, we present a combinatory chaos analysis of daily wavelet-filtered (denoised) S&P 500 returns (2000–2020) compared with respective surrogate datasets, Brownian motion returns and a Lorenz system realisation. We show that the dynamics of the S&P 500 return series consist of an almost equally divided combination of stochastic and deterministic chaos. The strange attractor of the S&P 500 return system is graphically displayed via Takens’ embedding and by spectral embedding in combination with Laplacian Eigenmaps. For the field of nonlinear and financial chaos research, we present a bibliometric analysis paired with citation network analysis. We critically discuss implications and future prospects.