arXiv:1105.2988cs.IT
Anatomy of a Bit: Information in a Time Series Observation
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Abstract
Appealing to several multivariate information measures---some familiar, some new here---we analyze the information embedded in discrete-valued stochastic time series. We dissect the uncertainty of a single observation to demonstrate how the measures' asymptotic behavior sheds structural and semantic light on the generating process's internal information dynamics. The measures scale with the length of time window, which captures both intensive (rates of growth) and subextensive components. We provide interpretations for the components, developing explicit relationships between them. We also identify the informational component shared between the past and the future that is not contained in a single observation. The existence of this component directly motivates the notion of a process's effective (internal) states and indicates why one must build models.
if you find this interesting you'll also find the publications of J.P Cruthfield interesting, he seem to have worked in this same institute up to 2004 before moving to UC Davis. he has 20+ years worth of papers on the topic, I keep procrastinating reading them esp the ones about…
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