Identification of measurement and intrinsic noise in time series through topological statistics criteria

Understanding the interplay between intrinsic and measurement noise is a key step in time series analysis, especially when a possible underlying deterministic dynamics is sought. A recent method, based on the statistical differentiability of the natural measure along the reconstructed trajectory, has been shown to be capable to detect the presence of intrinsic noise and to reveal high-dimensional determinism. Here we indicate how to extend the method to deal with series affected by measurement noise, which is the typical experimental situation. This is done by making joint tests of the statistical differentiability of the measure and of the statistical continuity of the series itself. The different levels observed in the latter allow us to discriminate between the two types of noise. In addition the results could provide interesting hints for the analysis of real physiological data.