Improved method for distinguishing determinism from randomness in the presence of noise

Abstract

This work presents an improved method for detecting determinism in time series. The method requires several input parameters, and a procedure for determining optimal values for these parameters is given. The method is applied to several types of noise and it is shown to be able to detect determinism for noise levels up to 70% - 80% of the magnitude of the signal of the dynamical system to which the noise is being added. The method is reliable for data sets as small as 256 data points. The method is also applied to data sets for which the source of noise is a chaotic system. In these cases, determinism is detected in the noise source itself.