Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices

TL;DR

This study reveals universal and nonuniversal allometric scaling behaviors in the visibility graphs of 30 world stock market indices, highlighting the influence of return distribution and correlations on network properties.

Contribution

It uncovers a universal allometric scaling law in minimal spanning trees of stock indices and analyzes the factors causing deviations in other spanning trees.

Findings

Universal allometric scaling in minimal spanning trees

Discrepancies due to fat-tailed returns and long-term correlations

Differences between stock indices and Brownian motions

Abstract

The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we investigate 30 world stock market indices through their visibility graphs by adopting the visibility algorithm to convert each single stock index into one visibility graph. A universal allometric scaling law is uncovered in the minimal spanning trees, whose scaling exponent is independent of the stock market and the length of the stock index. In contrast, the maximal spanning trees and the random spanning trees do not exhibit universal allometric scaling behaviors. There are marked discrepancies in the allometric scaling behaviors between the stock indices and the Brownian motions. Using surrogate time series, we find that these discrepancies are caused by the fat-tailedness of the return distribution, the nonlinear long-term correlation, and a coupling effect between these two influence factors.