@article{VoglRoetzel2022, author = {Vogl, Markus and R{\"o}tzel, Peter}, title = {Chaoticity Versus Stochasticity in Financial Markets: Are Daily S\&P 500 Return Dynamics Chaotic?}, series = {Communications in Nonlinear Science and Numerical Simulation}, volume = {2022}, journal = {Communications in Nonlinear Science and Numerical Simulation}, number = {Forthcoming}, pages = {1 -- 51}, year = {2022}, abstract = {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.}, subject = {Aktienrendite}, language = {en} } @techreport{VoglRoetzel2021, type = {Working Paper}, author = {Vogl, Markus and R{\"o}tzel, Peter}, title = {Chaoticity Versus Stochasticity in Financial Markets: Are Daily S\&P 500 Return Dynamics Chaotic?}, year = {2021}, abstract = {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.}, subject = {Kreditmarkt}, language = {en} }