Recurrence Quantification Analysis of Wavelet Pre-Filtered Index Returns

Abstract

We investigate the issue of deterministic vs. stochastic dynamics in financial time series. We demonstrate a way to to reveal nonstochastic dynamical structures in daily stock market index returns, combining Recurrence Quantification Analysis (RQA) and wavelet filtering. Assuming a dynamical system generating the returns sequences, we reproduce its dynamics from the data with minimum assumptions. We reconstruct the phase-space dynamics by time-delay embedding of the wavelet denoised returns, in order to apply the RQA. The results indicate that through wavelet pre-filtering we can obtain very clean sequences and reveal nonstochastic dynamics. Our results also suggest the existence of chaos. We provide both quantitative and qualitative evidence supporting our findings.