How to Determine the Redundancy of Noisy Chaotic Time Series

The mutual information and the redundancy are used in the time series analysis as tools to determine the best possible time-lag for successful phase space reconstruction. The known methods exhibit difficulties and inaccuracy when applied to noisy and small data sets. In this paper, we will introduce two methods to make a more reliable determination of the redundancy possible. Firstly, we will modify the Θ-function used in the correlation intergrals and, secondly, we will use the "Neural Gas" algorithm to calculate reference vectors and local radii, which enter the redundancy calculations. A clear differentiation between the redundancy and the mutual information on information theoretical background provides the path along which the new methods can be introduced and applied to the Mackey–Glass and Lorenz systems.