Evidence for deterministic nonlinear dynamics in financial time series data

Intra-day measurements of three time series (DJIA, gold fixings and USD-JPY exchange rates) are examined for evidence of deterministic nonlinear dynamics. Standard linear surrogate techniques and estimation of dynamic invariants demonstrate that linear noise models are insufficient to explain dynamic variability in intra-day returns. Therefore, the data may not be modeled as a monotonic nonlinear transformation of linearly filtered noise. Furthermore, a new nonlinear surrogate technique is employed to demonstrate that conditional heteroskedastic models are also insufficient to model this data. We conclude that the most likely model of the data is a nonlinear dynamical system driven by high dimensional dynamics (noise).