An investigation of chaos-oriented dimensionality algorithms applied to AR(1) processes

Discrimination between chaotic and stochastic processes is usually approached with second-order algorithms such as correlation integral or local intrinsic dimensionality. However, if these methods behave as expected for white Gaussian noise, they may fail for more structured processes. This fact is investigated in the case of AR(1) processes. Improvements to second-order algorithms are proposed by incorporating fourth-order informations, the idea being to track statistical independence beyond uncorrelation. The effectiveness of this new approach is illustrated on the same AR(1) processes