Multiscale correlation dimension method

Abstract

We propose a new method as an extension of the correlation dimension analysis by combining it with multiscale analysis taking into consideration the features in multiple time scales. We introduce and demonstrate multiscale correlation dimension analysis (MSCD) on several chaotic and stochastic time series in detail. We also study the choice of effective scaling filter as an alternative to the overlapping coarse-graining procedure we used for MSCD analysis and suggest the Gaussian filter according to its favorable performance and experiment it by assigning it for the second part of the study. Based on MSCD analysis, we further investigate CD and Hurst exponent relationship in multiscale on the same set of time series. We unveil a remarkable consistent patterns for the stochastic time series and describe it in a functional form. Consequently, the observed distinguishing patterns imply to opening up a new way of characterizing chaotic and stochastic time series.