Visibility Graph Analysis of Real-Life and GARCH-Simulated Financial Time-Series

Abstract

In this thesis, we will use the natural and horizontal visibility graph algorithms to look at financial time-series. We will apply the two algorithms to time-series generated from thirteen sets of simulations with the help of GARCH-processes, as well as ten subsets of daily data from S&P 500, both in its raw form, and in terms of returns. The five network statistics mean degree, average shortest path length, assortativity, local transitivity and global transitivity will be used in an attempt to see whether the visibility graph algorithms are in fact able to differentiate between time-series of different structures. This thesis will contribute to the literature with a more extensive investigation of the visibility graph’s behavior when applied to financial time-series than we have yet to see. The results obtained in this thesis will show that especially the natural visibility graph has the ability to differentiate between different time-series, and that it is an analysis tool that deserves more research in the future.