Recurrence quantification analysis of wavelet pre-filtered index returns

In this paper we investigate for the presence of non-stochastic, possibly nonlinear deterministic dynamical cycles in financial time series. Evidence of nonlinear dynamics is revealed in denoised daily stock market index returns for six countries by combining Recurrence Quantification Analysis (RQA: see Zbilut and Webber (J. Appl. Phys. 76(2) (1994) 965)) and wavelet filtering. Quantitative and qualitative results indicate that through wavelet pre-filtering we can obtain a clearer view of the underlying dynamical structure of returns generating processes. Our results also suggest the existence of high dimensional deterministic dynamics, unstable periodic orbits and chaos.