Using the pointwise dimension to filter time series

This paper provides an insight into dimension analysis from time series. In particular, we propose a procedure based on the pointwise dimension in order to extract, for each embedding dimension, the subset of points in the phase space (and the corresponding ones in the time series) which give rise to the scaling behaviour. We may consider the output time series as the result of a filtering process, based on correlations of points in the phase-space domain. Furthermore, the procedure gives the statistics of points which determine the scaling behaviour.