  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.
