Related papers: A statistical test of market efficiency based on i…
We servey a series of investigations of optimal testing of multiple hypotheses conserning various multiobject models. These studies are a bright instance of application of methods and technics developed in Shannon information theory to…
The efficient market hypothesis has been considered one of the most controversial arguments in finance, with the academia divided between who claims the impossibility of beating the market and who believes that it is possible to gain over…
Information theory has provided foundations for the theories of several application areas critical for modern society, including communications, computer storage, and AI. A key aspect of Shannon's 1948 theory is a sharp lower bound on the…
Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters,…
We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed…
The statistical analysis of data stemming from dynamical systems, including, but not limited to, time series, routinely relies on the estimation of information theoretical quantities, most notably Shannon entropy. To this purpose, possibly…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
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…
Markets efficiency implies that the stock returns are intrinsically unpredictable, a property that makes markets comparable to random number generators. We present a novel methodology to investigate ultra-high frequency financial data and…
The rapid scaling of artificial intelligence models has revealed a fundamental tension between model capacity (storage) and inference efficiency (computation). While classical information theory focuses on transmission and storage limits,…
A class of information inequalities, called Shannon-type inequalities (STIs), can be proven via a computer software called ITIP. In previous work, we have shown how this technique can be utilized to Fourier-Motzkin elimination algorithm for…
Empirical evidence suggests that even the most competitive markets are not strictly efficient. Price histories can be used to predict near future returns with a probability better than random chance. Many markets can be considered as {\it…
We study the informational efficiency of a market with a single traded asset. The price initially differs from the fundamental value, about which the agents have noisy private information (which is, on average, correct). A fraction of…
We present results on simulations of a stock market with heterogeneous, cumulative information setup. We find a non-monotonic behaviour of traders' returns as a function of their information level. Particularly, the average informed agents…
In this paper, I expand Shannon's definition of entropy into a new form of entropy that allows integration of information from different random events. Shannon's notion of entropy is a special case of my more general definition of entropy.…
Despite the wide usage of information as a concept in science, we have yet to develop a clear & concise scientific definition. This paper is aimed at laying the foundations for a new theory concerning the mechanics of information alongside…
In this article, the long-term behavior of the stock market index of the New York Stock Exchange is studied, for the period 1950 to 2013. Specifically, the CRSP Value-Weighted and CRSP Equal-Weighted index are analyzed in terms of market…
The advances and development of various machine learning techniques has lead to practical solutions in various areas of science, engineering, medicine and finance. The great choice of algorithms, their implementations and libraries has…
There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as…
This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…