Self-organized Criticality of Individual Companies: An Empirical Study

The stock market is a typically complex and self-interacting system that in many aspects it shows the characteristic of self-organized criticality (SOC). In the present work we mainly investigate the SOC properties of individual companies. Price volatility can be served as an analogy of "avalanche" in the classical sand-pile model and different volatility statistics have different power law behaviors. We mainly analyze the distributions of the return and its ramificate statistics, both theoretical and experimental. The empirical study of the Chinese 5-min trading data (from 2005/7/8 to 2006/2/8) shows that some volatility statistics did show significant power law behaviors while some other volatility statistics show asymptotic power law behaviors and do not accord with the classical SOC model, which might be SOC affected by noise, sub-critical or even chaos. Furthermore, we find that cumulative volatility statistics are much more significant than the original statistics and the high-order volatilty statistics present an inherent multifractality.