Hodge Decomposition of Information Flow on Small-World Networks

Causal Hierarchy in the Financial Market Network-Uncovered by the Helmholtz-Hodge-Kodaira Decomposition

Granger causality can uncover the cause-and-effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz-Hodge-Kodaira decomposition can split them into rotational and gradient components which reveal the hierarchy of the Granger causality flow. Using Kenneth French's business sector return time series, it is revealed that during the COVID crisis, precious metals and pharmaceutical products were causal drivers of the financial network. Moreover, the estimated Granger causality network shows a high connectivity during the crisis, which means that the research presented here can be especially useful for understanding crises in the market better by revealing the dominant drivers of crisis dynamics.

Parallelism Strategies for Big Data Delayed Transfer Entropy Evaluation

Generated and collected data have been rising with the popularization of technologies such as Internet of Things, social media, and smartphone, leading big data term creation. One class of big data hidden information is causality. Among the tools to infer causal relationships, there is Delay Transfer Entropy (DTE); however, it has a high demanding processing power. Many approaches were proposed to overcome DTE performance issues such as GPU and FPGA implementations. Our study compared different parallel strategies to calculate DTE from big data series using a heterogeneous Beowulf cluster. Task Parallelism was significantly faster in comparison to Data Parallelism. With big data trend in sight, these results may enable bigger datasets analysis or better statistical evidence.