AUTHOR=Yadav Gaurang Singh , Guha Apratim , Chakrabarti Anindya S. 

TITLE=Measuring Complexity in Financial Data

JOURNAL=Frontiers in Physics

VOLUME=Volume 8 - 2020

YEAR=2020

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00339

DOI=10.3389/fphy.2020.00339

ISSN=2296-424X

ABSTRACT=Stock market is a canonical example of complex systems, where a large number of interacting
agents lead to joint evolution of stock returns and the collective market behavior exhibits
emergent properties. However, quantifying complexity in the stock market data has been a
challenging task. In this report, we explore four different measures to characterize the intrinsic
complexity by evaluating structural relationship among stock returns. The first two measures
are based on linear and non-linear comovement structure (accounting for contemporaneous and
Granger-causal relationships), the third one is based on algorithmic complexity and the fourth
one is based on spectral analysis of interacting dynamical systems. In our dataset comprising
daily prices of a large number of stocks in the complete historical data of NASDAQ (1972-
2018), we see that the third and fourth measures are able to identify the largest global economic
downturn in 2007-09 and associated spillovers, substantially more accurately than the first two
measures. Finally, we conclude this brief research report with discussions on implications of such
quantification for risk management in complex systems.