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We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchronization is determined by both the process's internal organization and by an observer's model of it. We analyze these components using the convergence of state-block and block-state… (More)

Accurately determining dependency structure is critical to discovering a system's causal organization. We recently showed that the transfer entropy fails in a key aspect of this—measuring information flow—due to its conflation of dyadic and polyadic relationships. We extend this observation to demonstrate that this is true of all such Shannon information… (More)

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… (More)

The introduction of the partial information decomposition generated a flurry of proposals for defining an intersection information that quantifies how much of " the same information " two or more random variables specify about a target random variable. As of yet, none is wholly satisfactory. A palatable measure of intersection information would provide a… (More)

We consider two important time scales-the Markov and cryptic orders-that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the ε-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from… (More)

The hallmark of deterministic chaos is that it creates information—the rate being given by the Kolmogorov-Sinai metric entropy. Since its introduction half a century ago, the metric entropy has been used as a unitary quantity to measure a system's intrinsic unpredictability. Here, we show that it naturally decomposes into two structurally meaningful… (More)

We investigate a stationary process's crypticity--a measure of the difference between its hidden state information and its observed information--using the causal states of computational mechanics. Here, we motivate crypticity and cryptic order as physically meaningful quantities that monitor how hidden a hidden process is. This is done by recasting previous… (More)

Modeling a temporal process as if it is Markovian assumes that the present encodes all of a process's history. When this occurs, the present captures all of the dependency between past and future. We recently showed that if one randomly samples in the space of structured processes, this is almost never the case. So, how does the Markov failure come about?… (More)

We study dynamical reversibility in stationary stochastic processes from an information-theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional correlations. In particular, we examine stationary processes represented or generated by edge-emitting, finite-state… (More)

This paper provides insight into when, why, and how forecast strategies fail when they are applied to complicated time series. We conjecture that the inherent complexity of real-world time-series data—which results from the dimension, nonlinearity, and non-stationarity of the generating process, as well as from measurement issues like noise, aggregation,… (More)