On the detection of determinism in a time series

The nonlinearly scaled distributions of the strengths of the orthogonal mod es in the data of a time series are compared with that derived from its sur rogate counterpart to assess its chaoticity or the stochastic nature. Chaot icity manifests in the relatively decreasing strengths of the weaker modes with increasing dimension of the orthogonal spaces mapping the process. The distributions of the strengths of the modes for the data and the surrogate are compared statistically. Singular value decomposition is used for the i mplementation. The ability of the proposed method to distinguish between ch aotic and stochastic dynamics is demonstrated through a number of simulated series (including linear and nonlinear stochastic noise, and processes des cribed by Lorenz, Rossler, and Mackey-Glass equations, Henon map and Ecolog ical map), and some real life examples. (C) 1999 Elsevier Science B.V. All rights reserved.