Exact results of the limited penetrable horizontal visibility graph associated to random time series and its application

By Minggang Wang, A. M. Vilela, Ruijin Du, Longfeng Zhao, Gaogao Dong, Lixin Tian, H. Eugene Stanley. 2017

39 citations recorded by the source corpus.

The limited penetrable horizontal visibility algorithm is an analysis tool that maps time series into complex networks and is a further development of the horizontal visibility algorithm. This paper presents exact results on the topological properties of the limited penetrable horizontal visibility graph associated with independent and identically distributed (i:i:d:) random series. We show that the i.i.d: random series maps on a limited penetrable horizontal visibility graph with exponential degree distribution, independent of the probability distribution from which the series was generated. We deduce the exact expressions of mean degree and clustering coefficient, demonstrate the long distance visibility property of the graph and perform numerical simulations to test the accuracy of our theoretical results. We then use the algorithm in several deterministic chaotic series, such as the logistic map, H´enon map, Lorenz system, energy price chaotic system and the real crude oil price. Our results show that the limited penetrable horizontal visibility algorithm is efficient to discriminate chaos from uncorrelated randomness and is able to measure the global evolution characteristics of the real time series.

Subfields: Computer Networks and Communications, Economics and Econometrics, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Ruijin Du
2. H. Eugene Stanley
3. Lin Chen
4. Chao Wang
5. Minggang Wang

In Economics and Econometrics

1. Ruijin Du
2. Minggang Wang
3. H. Eugene Stanley
4. Lin Chen
5. Chao Wang
6. Zhilin Qiao
7. Ladislav Kristoufek
8. Ling-Yun He

In Statistical and Nonlinear Physics

1. Minggang Wang
2. H. Eugene Stanley
3. Ladislav Kristoufek
4. Mark Newman
5. Ling-Yun He
6. Shu-Peng Chen

Citations in the corpus

• Which Artificial Intelligence Algorithm Better Predicts the Chinese Stock Market? (2018, methodology): “Some other methods have been applied to time-series analysis [27]–[29].”
• Complex network approaches to nonlinear time series analysis (2019, unknown): “has an exponential degree distribution [250].”