Comparative analysis of distance measures in stock network construction and cluster analysis

The mutual information (MI) metric and the Pearson correlation metric are both widely used in cluster analysis and stock network construction. This paper presents a detailed comparison between the MI metric and the Pearson correlation metric. To detect nonlinear relationships, polynomial and natural cubic spline regressions are proposed as alternatives to the MI metric. The methodology for computing model-fitting indices for determining network adjacencies is explained in detail, along with a comparison of the results with the MI methodology. This study employs two data sets derived from the log returns of the daily adjusted closing prices of 402 stocks in the S%P500 index to measure the impact of a financial crisis on nonlinearity: one covering the crisis period from January 2007 to December 2009, and the other covering the non-crisis period between January 2012 and December 2015. The local and global properties of hierarchical stock networks are compared using the minimum spanning tree for each distance measure. The graph-theoretic internal cluster validity indices and external indices are also used to investigate the relationship between the performance of the community detection algorithm and the selection of metrics.