Related papers: Renyi's information transfer between financial tim…
In this article, we review a general theoretical framework of thermodynamics of information on the basis of Bayesian networks. This framework can describe a broad class of nonequilibrium dynamics of multiple interacting systems with complex…
Financial markets are dynamic, interconnected systems where local shocks can trigger widespread instability, challenging portfolio managers and policymakers. Traditional correlation analysis often miss the directionality and temporal…
The Shannon entropy is a widely used summary statistic, for example, network traffic measurement, anomaly detection, neural computations, spike trains, etc. This study focuses on estimating Shannon entropy of data streams. It is known that…
The nature of neural codes is central to neuroscience. Do neurons encode information through relatively slow changes in the emission rates of individual spikes (rate code), or by the precise timing of every spike (temporal codes)? Here we…
We present a symmetry analysis of the distribution of variations of different financial indices, by means of a statistical procedure developed by the authors based on a symmetry statistic by Einmahl and Mckeague. We applied this statistical…
The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph \cite{DM1,M}. After Shannon introduced the definition of entropy to information and communication, many generalizations of the entropy…
Taking into account extremum of a Helmholtz free energy in the equilibrium state of a thermodynamic system the Renyi entropy is derived from the Boltzmann entropy by the same way as the Helmholtz free energy from the Hamiltonian. The…
Data from social media are providing unprecedented opportunities to investigate the processes that rule the dynamics of collective social phenomena. Here, we consider an information theoretical approach to define and measure the temporal…
We consider the problem of approximating the empirical Shannon entropy of a high-frequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is…
This paper considers an information bottleneck problem with the objective of obtaining a most informative representation of a hidden feature subject to a R\'enyi entropy complexity constraint. The optimal bottleneck trade-off between…
Bounds on information combining are entropic inequalities that determine how the information, or entropy, of a set of random variables can change when they are combined in certain prescribed ways. Such bounds play an important role in…
Whether the system under study is a shoal of fish, a collection of neurons, or a set of interacting atmospheric and oceanic processes, transfer entropy measures the flow of information between time series and can detect possible causal…
One of the major issues studied in finance that has always intrigued, both scholars and practitioners, and to which no unified theory has yet been discovered, is the reason why prices move over time. Since there are several well-known…
Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences,…
Transfer entropy (TE) is a popular measure of information flow found to perform consistently well in different settings. Symbolic transfer entropy (STE) is defined similarly to TE but on the ranks of the components of the reconstructed…
The symbolic dynamics technique is well-known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully…
We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs--Shannon entropy into more general framework - Renyi's information entropy. We address the…
Transfer entropy is capable of capturing nonlinear source-destination relations between multi-variate time series. It is a measure of association between source data that are transformed into destination data via a set of linear…
Here we present a novel approach to statistical analysis of financial time series. The approach is based on $n$-grams frequency dictionaries derived from the quantized market data. Such dictionaries are studied by evaluating their…
We discuss the interest of escort distributions and R\'enyi entropy in the context of source coding. We first recall a source coding theorem by Campbell relating a generalized measure of length to the R\'enyi-Tsallis entropy. We show that…