Complexity in financial asset returns: evidence from the compass rose

Abstract

The compass rose pattern in financial data may indicate the presence of a nonlinear, possibly chaotic, data generating mechanism. The analysis of three key financial asset and denoised returns, gold, the Great British Pound/US dollar spot exchange rate, and the Standard & Poor's 500 stock index, reveals that over four equivalent subperiods, from 1996 to 2015, the compass rose pattern changes. This finding provides an opportunity to establish how noise affects financial time series. We conclude that the compass rose pattern is unlikely the product of an underlying nonlinear structure, since there is evidence of nonlinearity in all time periods, even those where the compass rose pattern is not evident. Therefore, the compass rose patterns, seen in the denoised data, suggest that the presence of noise masks the underlying dynamics of the asset returns.