Abstract
Information theory is a well-established method for the study of many phenomena and more than 70 years after Claude Shannon first described it in A Mathematical Theory of Communication it has been extended well beyond Shannon’s initial vision. It is now an interdisciplinary tool that is used from ‘causal’ information flow to inferring complex computational processes and it is common to see it play an important role in fields as diverse as neuroscience, artificial intelligence, quantum mechanics, and astrophysics. In this article, I provide a selective review of a specific aspect of information theory that has received less attention than many of the others: as a tool for understanding, modelling, and detecting non-linear phenomena in finance and economics. Although some progress has been made in this area, it is still an under-developed area that I argue has considerable scope for further development.
Highlights
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At the individual agent level Dinis et al [12] studied phase transitions in optimal betting strategies using the Kelly criterion. This opinion piece argues for an alternative use of information theory that has been used earlier but has yet to make a significant impact in the field of economics or information theory: As a tool for the analysis of “critical phenomena” in economics
This becomes relevant to critical phenomena because of the relationship with Scheffer et al.’s work and because transfer entropy (TE) peaks before the phase-transition in the two-dimensional Ising model [25], where the Gaussian assumption no longer holds, i.e., TE becomes a candidate for the analysis of phase transitions at precisely the point where the relationship between
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. At the individual agent level Dinis et al [12] studied phase transitions in optimal betting strategies using the Kelly criterion This opinion piece argues for an alternative use of information theory that has been used earlier but has yet to make a significant impact in the field of economics or information theory: As a tool for the analysis of “critical phenomena” in economics. It follows on from earlier work I have completed applying the notion of critical phenomena to the abrupt breaks in time series data, such as market crashes, such as the 1987 crash [13], the Asian crisis of 1997 [14], the build up to the housing crisis of 2007 [15], and the COVID-19 crisis of 2020–2021 [16], all of which made use of information theory in its various forms. These two points are covered in the two sections and some final points are discussed at the end
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