Abstract
In this paper, 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 observe a clear distinction of the nature of the underlying time series dynamics by applying a novel and combinatory chaos analysis framework by comparing the wavelet-filtered S&P 500 returns with surrogate datasets, Brownian motion returns, and a Lorenz system realisation. Furthermore, we are the first to observe the strange attractor of the daily S&P 500 return system graphically via Takens’ embedding and a spectral embedding in combination with Laplacian eigenmaps. Finally, we critically discuss the implications and future prospects of financial forecasting.
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