  A scheme is presented to extract detailed dynamical signatures from
successive measurements of complex systems. Relative entropy based time series
tools are used to quantify the gain in predictive power of increasing past
knowledge. By lossy compression, data is represented by increasingly coarsened
symbolic strings. Each compression resolution is modeled by a machine: a finite
memory transition matrix. Applying the relative entropy tools to each machine's
memory exposes correlations within many time scales. Examples are given for
cardiac arrhythmias and different heart conditions are distinguished.
