Data Compression, Dynamics, and Stationarity
One of the main themes of this book is the considerable progress that has been made in modeling data from nonlinear systems that may be affected by noise. In this chapter, we describe a modeling method based on an idealization that gives fast algorithms with known properties based on rigorous results from data-compression theory. The idealization is that the system outputs symbols from a finite alphabet, rather than outputting a real number; we also make a reasonable assumption which is the discrete analogue of the standard embedding theorem. The models that result can be used to simulate and to estimate many of the usual dynamically interesting quantities such as topological entropy. They are also well-suited for a specific new application: testing the stationarity of time-series of discrete symbols, whether two data streams appear to originate from the same underlying unknown dynamical system.
KeywordsData Compression Strange Attractor Code Length Topological Entropy Chaotic Time Series
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