Exploring stock markets dynamics: a two-dimensional entropy approach in return/volume space

This paper presents an entropy-based analysis of returns and trading volumes in stock markets. We introduce a measure of entropy in the return/volume space, leveraging Shannon’s entropy, Theil’s index, Relative Entropy, Tsallis distribution, and the Kullback-Leibler Divergence. We assess one- and two-dimensional returns and volume distributions, separately and jointly. This exploratory study aims to discover and understand patterns and relationships in data that are not yet well-defined in the literature. By exploring entropy measures, we identify mutual relations between returns and volume in financial data during global shocks such as the COVID-19 pandemic and the war in Ukraine. Revealing entropy changes in the return/volume space consistent with changes in the real economy allows for the inclusion of a new variable in machine learning algorithms that reflects the system’s unpredictability.