Correlation and interdependence structure in stock market: Based on information theory and complex networks

Abstract

Mutual information (MI) and transfer entropy (TE) are employed to measure correlation and interdependence between stocks. Based on algorithms of Minimal Spanning Tree (MST) and Planar Maximally Filtered Graph (PMFG), redundant information contained in fully connected networks represented by MI and TE matrices are filtered and according networks are constructed. It is found that the MST of MI constructed on full sample of data, i.e. from January 1, 2007 to December 30, 2016, follows the power-law distribution. Most MSTs constructed on subsamples, a window length of about one calendar year rolling for one calendar month, also follow the power-law distribution. Small-world behavior of PMFGs constructed on both MI and TE calculated from all sub-samples is observed. We further find that correlation between intra-sector stocks is generally greater than its inter-sector equivalent. However, stocks from sectors with large intra-sector interdependence also interact intensively with stocks from other sectors. These results suggest different characteristics of intra- and inter-sector correlation and interdependence structure in the stock market.