Path-Based Visibility Graph Kernel and Application for the Borsa Istanbul Stock Network

Abstract

Using networks to analyze time series has become increasingly popular in recent years. Univariate and multivariate time series can be mapped to networks in order to examine both local and global behaviors. Visibility graph-based time series analysis is proposed herein; in this approach, individual time series are mapped to visibility graphs that characterize relevant states. Companies listed on the emerging market index Borsa Istanbul 100 (BIST 100) had their market visibility graphs collected. To further account for the local extreme values of the underlying time series, we constructed a novel kernel function of the visibility graphs. Via the provided novel measure, sector-level and sector-to-sector analyses are conducted using the kernel function associated with this metric. To examine sectoral trends, the COVID-19 crisis period was included in the study’s data set. The findings indicate that an effective strategy for analyzing financial time series has been devised.

Keywords

• visibility graphs
• stock market network
• graph kernel