On the detection of determinism in a time series

The nonlinearly scaled distributions of the strengths of the orthogonal modes in the data of a time series are compared with that derived from its surrogate counterpart to assess its chaoticity or the stochastic nature. Chaoticity 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 implementation. The ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated series (including linear and nonlinear stochastic noise, and processes described by Lorenz, Rössler, and Mackey–Glass equations, Hénon map and Ecological map), and some real life examples