Measuring Complexity in Financial Data - Yadav, Gaurang Singh; Guha, Apratim; Chakrabarti, Anindya S. (Frontiers in Physics, 2020)
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.