Smoothness implies determinism in time series: A measure based approach

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to stochasticity. Numerical results for partially surrogated time series and series derived from the stochastic Lorenz model illustrate the usefulness of the method proposed here. The method is shown to work also for high-dimensional systems. [S0031-9007(98)07686-8].