Anatomy of a Bit: Information in a Time Series Observation

Details Anatomy of a Bit: Information in a Time Series Observation Anatomy of a Bit: Information in a Time Series Observation

2011-05-16

arxiv.org/abs/1105.2988v1

Computer Science

Information Theory

15 pages, 12 figures, 2 tables; http://cse.ucdavis.edu/~cmg/compmech/pubs/anatomy.htm

Scientific paper

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.

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