Price clustering and discreteness: is there chaos behind the noise?

We investigate the “compass rose” patterns introduced by Crack and Ledoit (J. Finance 51(2)(1996) 751) as revealed in phase portraits (delay plots) of stock returns. The structures observed in these diagrams have been attributed mainly to price clustering and discreteness and the tick size. Using wavelet-based denoising, we examine the noise-free versions of a set of FTSE100 stock returns time series. We reveal evidence of non-periodic cyclical dynamics. As a second stage we apply surrogate data analysis on the original and denoised stock returns. Our results suggest that there is a strong nonlinear and possibly deterministic signature in the data generating processes of the stock returns sequences.