Deterministic Nonlinearity Research Articles

Determinism in Financial Time Series

The attractive possibility that financial indices may be chaotic has been the subject of much study. In this paper we address two specific questions: Masked by stochasticity, do financial data exhibit deterministic nonlinearity?, and If so, so what?. We examine daily returns from three financial indicators: the Dow Jones Industrial Average, the London gold fixings, and the USD-JPY exchange rate. For each data set we apply surrogate data methods and nonlinearity tests to quantify determinism over a wide range of time scales (from 100 to 20,000 days). We find that all three time series are distinct from linear noise or conditional heteroskedastic models and that there therefore exists detectable deterministic nonlinearity that can potentially be exploited for prediction.

Deterministic nonlinearity in the stock returns of major European equity markets and the United States

AbstractBy using recently developed statistical tools designed to overcome some of the limitations often associated with financial data, this study attempts to detect low‐dimensional deterministic chaos in five major European stock markets and the United States. Country indexes exhibiting low‐dimensional deterministic chaos may contain some informational inefficiency; thus, it may be possible to use nonlinear dynamics to predict future stock returns. The results do not provide evidence of the existence of low‐dimensional chaotic systems in any of the examined indexes. As such, the notion of market efficiency in the examined indexes is not threatened by the findings of this study.

Deterministic Non-linear Dynamics in Phycomyces Sporangiophores

The growth rate of the Phycomyces sporangiophore fluctuates under constant environmental conditions. To test for deterministic non-linearity in these growth-rate fluctuations, we applied variants of several recently developed techniques. We found that wild-type sporangiophores have a significant non-linear component, whereas non-linear contributions to the growth fluctuations of a stiff ( madE) mutant are less significant. This difference may be caused by the dominance of a linear 10·4 min rhythm in the mutant's growth rate. Previous system analysis studies, which involved stimulation by dynamically changing light intensity, identified a non-linearity near the input of the Phycomyces sensory system. Our results, which involve analysis of growth-rate fluctuations under constant environmental conditions, demonstrate the presence of deterministic non-linearity even in the absence of sensory stimulation.