Time Series Analysis Based on Visibility Graph Theory

The dynamics of a complex system is usually recorded in the form of time series. In recent years, the visibility graph algorithm and the horizontal visibility graph algorithm have been recently introduced as the mapping between time series and complex networks. Transforming time series into the graphs, the algorithms allows applying the methods of graph theoretical tools for characterizing time series, opening the possibility of building fruitful connections between time series analysis, nonlinear dynamics, and graph theory. This paper analyzes mainly the topological properties of visibility graphs and horizontal visibility graphs associated to random series and fractional Brownian motions series, with a special emphasis on degree distribution of the associated graphs. As an example, this paper study the visibility graph and horizontal visibility graph constructed from the total daily turnover of stock market, and unveil that the degree distribution of visibility graph has power-law tails, and the degree distribution of horizontal visibility graph has exponential tail.