Physics – Data Analysis – Statistics and Probability
Scientific paper
2005-03-08
Phys. Rev. E 71, 056106 (2005).
Physics
Data Analysis, Statistics and Probability
9 pages, 7 figures
Scientific paper
10.1103/PhysRevE.71.056106
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical systems. We compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series. In particular, we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function, on the interval whereto the recurrences are observed, and on the temporal correlations of time series. In the case of long-term correlations, we verify the validity of the stretched exponential distribution, which is uniquely defined by the exponent $\gamma$, at the same time showing that it is restricted to the class of linear long-term correlated processes. Simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different $\gamma$, which shows a lack of invariance under the change of observables.
Altmann Eduardo G.
Kantz Holger
No associations
LandOfFree
Recurrence time analysis, long-term correlations, and extreme events does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Recurrence time analysis, long-term correlations, and extreme events, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Recurrence time analysis, long-term correlations, and extreme events will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-403769