A non-subjective approach to the GP algorithm for analysing noisy time series

We present an adaptation of the standard Grassberger–Proccacia (GP) algorithm for estimating the correlation dimension of a time series in a non-subjective manner. The validity and accuracy of this approach are tested using different types of time series, such as those from standard chaotic systems, pure white and colored noise and chaotic systems with added noise. The effectiveness of the scheme in analysing noisy time series, particularly those involving colored noise, is investigated. One interesting result we have obtained is that, for the same percentage of noise addition, data with colored noise is more distinguishable from the corresponding surrogates than data with white noise. As examples of real life applications, analyses of data from an astrophysical X-ray object and a human brain EEG are presented.