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We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol…

Statistical Finance · Quantitative Finance 2016-09-15 Lucio Maria Calcagnile , Fulvio Corsi , Stefano Marmi

In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and in the Ornstein-Uhlenbeck context. Here…

Probability · Mathematics 2019-12-12 Samuel Herrmann , Nicolas Massin

Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is…

Machine Learning · Statistics 2023-05-10 Hiroshi Yamashita , Hideyuki Suzuki , Kazuyuki Aihara

Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…

Information Theory · Computer Science 2024-11-06 Bill Kay , Audun Myers , Thad Boydston , Emily Ellwein , Cameron Mackenzie , Iliana Alvarez , Erik Lentz

We determine the amount of information contained in a time series of price returns at a given time scale, by using a widespread tool of the information theory, namely the Shannon entropy, applied to a symbolic representation of this time…

Statistical Finance · Quantitative Finance 2022-08-26 Xavier Brouty , Matthieu Garcin

A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…

Quantum Physics · Physics 2011-11-14 Akimasa Miyake

We present an algorithmic approach to estimate the value distributions of random variables of probabilistic loops whose statistical moments are (partially) known. Based on these moments, we apply two statistical methods, Maximum Entropy and…

It is well known that to estimate the Shannon entropy for symbolic sequences accurately requires a large number of samples. When some aspects of the data are known it is plausible to attempt to use this to more efficiently compute entropy.…

Data Analysis, Statistics and Probability · Physics 2018-05-18 Andrew D. Back , Daniel Angus , Janet Wiles

Maximum entropy method is a constructive criterion for setting up a probability distribution maximally non-committal to missing information on the basis of partial knowledge, usually stated as constrains on expectation values of some…

Statistical Mechanics · Physics 2015-07-20 Jorge Fernandez-de-Cossio , Jorge Fernandez-de-Cossio Diaz

In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…

Data Structures and Algorithms · Computer Science 2013-05-02 Mohit Singh , Nisheeth K. Vishnoi

Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…

Probability · Mathematics 2018-01-23 Alois Pichler , Ruben Schlotter

This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes the pragmatic elements in the derivation. An epistemic notion of information is defined in…

Data Analysis, Statistics and Probability · Physics 2021-08-04 Ariel Caticha

Bayesian, classical, and extended maximum likelihood approaches to estimation of upper limits in experiments with small numbers of signal events are surveyed. The discussion covers only experiments whose outcomes are well described by a…

High Energy Physics - Experiment · Physics 2011-07-19 Ilya Narsky

In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on…

Statistical Mechanics · Physics 2024-08-12 Ivan N. Burenev , Satya N. Majumdar , Alberto Rosso

Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…

Methodology · Statistics 2023-03-22 Ioannis Papageorgiou , Ioannis Kontoyiannis

Entropy is a very useful concept from physics that tries to explain how a system behaves from a point of view of the thermodynamics. However, there are two ways to explain entropy, and it depends on if we are studying a microsystem or a…

General Finance · Quantitative Finance 2024-07-02 Martin Pomares Calero

Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…

Statistics Theory · Mathematics 2019-08-06 Alexander L Young , David B Dunson

Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…

Chaotic Dynamics · Physics 2009-11-10 Milan Rajkovic

A classical longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using…

Combinatorics · Mathematics 2023-03-14 Tomer M. Schlank , Ran J. Tessler , Amitai Netser Zernik

In this tutorial we review the essential arguments behing entropic inference. We focus on the epistemological notion of information and its relation to the Bayesian beliefs of rational agents. The problem of updating from a prior to a…

Data Analysis, Statistics and Probability · Physics 2015-05-20 Ariel Caticha