Applying Visibility Graphs to Classify Time Series

The horizontal visibility algorithm was recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the powerful tools of graph theory. Recent works have shown that the visibility graphs inherit several degrees of correlations from their associated series, and therefore such graph theoretical characterization is in principle possible. However, both the mathematical grounding of this promising theory and its applications are in its infancy. Following this line, here we address the question of detecting hidden periodicity in series polluted with a certain amount of noise. We first put forward some generic properties of horizontal visibility graphs which allow us to define a (graph theoretical) noise reduction filter. Accordingly, we evaluate its performance for the task of calculating the period of noisy periodic signals, and compare our results with standard time domain (autocorrelation) methods. Finally, potentials, limitations and applications are discussed.

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Multifractal characterisation of particulate matter (PM10) time series in the Caribbean basin using visibility graphs

Atmospheric Pollution Research ◽

10.1016/j.apr.2020.08.027 ◽

2020 ◽

Author(s):

Thomas Plocoste ◽

Rafael Carmona-Cabezas ◽

Francisco José Jiménez-Hornero ◽

Eduardo Gutiérrez de Ravé ◽

Rudy Calif

Keyword(s):

Time Series ◽

Particulate Matter ◽

Caribbean Basin ◽

Visibility Graphs ◽

The Caribbean

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Fast transformation from time series to visibility graphs

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.4927835 ◽

2015 ◽

Vol 25 (8) ◽

pp. 083105 ◽

Cited By ~ 13

Author(s):

Xin Lan ◽

Hongming Mo ◽

Shiyu Chen ◽

Qi Liu ◽

Yong Deng

Keyword(s):

Time Series ◽

Visibility Graphs

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Could network analysis of horizontal visibility graphs be faithfully used to infer long-term memory properties in real-world time series?

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2019.104908 ◽

2019 ◽

Vol 79 ◽

pp. 104908 ◽

Cited By ~ 1

Author(s):

Yu Huang ◽

Qimin Deng ◽

Zuntao Fu

Keyword(s):

Time Series ◽

Network Analysis ◽

Real World ◽

Long Term Memory ◽

Term Memory ◽

Horizontal Visibility ◽

Visibility Graphs

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VISIBILITY GRAPHS FOR TIME SERIES CONTAINING DIFFERENT COMPONENTS

Fluctuation and Noise Letters ◽

10.1142/s0219477511000636 ◽

2011 ◽

Vol 10 (04) ◽

pp. 371-379 ◽

Cited By ~ 6

Author(s):

JINGCHAO QI ◽

JIANYONG WANG ◽

JIANBO WANG ◽

QIN XIAO ◽

HUIJIE YANG

Keyword(s):

Time Series ◽

Power Law ◽

Real World ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Visibility Graphs ◽

Hurst Exponents

We consider the visibility graphs for superpositions of fractional Brownian motions with different Hurst exponents. It is found that the degree distributions obey power-law. The components with lower Hurst exponents dominate the heterogeneity behaviors of the visibility graphs. These findings are helpful for us to understand the characteristics of visibility graphs for real-world time series.

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Visibility Graph Analysis of IOTA and IoTeX Price Series: An Intentional Risk-Based Strategy to Use 5G for IoT

Electronics ◽

10.3390/electronics10182282 ◽

2021 ◽

Vol 10 (18) ◽

pp. 2282

Author(s):

Alberto Partida ◽

Regino Criado ◽

Miguel Romance

Keyword(s):

Time Series ◽

Information Security ◽

Complex Networks ◽

Directed Acyclic Graph ◽

Price Volatility ◽

Price Series ◽

Visibility Graphs ◽

Iot Platforms ◽

Visibility Graph Analysis ◽

The Impact

The transformation of time series into complex networks through visibility graphs is an innovative way to study time-based events. In this work, we use visibility graphs to transform IOTA and IoTeX price volatility time series into complex networks. Our aim is twofold: first, to better understand the markets of the two most capitalised Internet of Things (IoT) platforms at the time of writing. IOTA runs on a public directed acyclic graph (DAG) and IoTeX on a blockchain. Second, to suggest how 5G can improve information security in these two key IoT platforms. The analysis of the networks created by the natural and horizontal visibility graphs shows, first, that both IOTA and IoTeX are still at their infancy in their development, with IoTex seemingly developing faster. Second, both IoT tokens form communities in a hierarchical structure, and third, 5G can accelerate their development. We use intentional risk management as a lever to understand the impact of 5G on IOTA and IoTeX. Our results lead us to provide a set of design recommendations that contribute to improving information security in future 5G-based IoT implementations.

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Assessing Time Series Reversibility through Permutation Patterns

10.20944/preprints201808.0083.v1 ◽

2018 ◽

Cited By ~ 1

Author(s):

Massimiliano Zanin ◽

Alejandro Rodríguez González ◽

Ernestina Menasalvas Ruiz ◽

David Papo

Keyword(s):

Time Series ◽

Time Reversal ◽

Financial Time Series ◽

Statistical Tests ◽

Fundamental Property ◽

Permutation Entropy ◽

Permutation Patterns ◽

Visibility Graphs ◽

Time Irreversibility ◽

Financial Data Analysis

Time irreversibility, i.e. the lack of invariance of the statistical properties of a system under time reversal, is a fundamental property of all systems operating out of equilibrium. Time reversal symmetry is associated with important statistical and physical properties and is related to the predictability of the system generating the time series. Over the past fifteen years, various methods to quantify time irreversibility in time series have been proposed, but these can be computationally expensive. Here we propose a new method, based on permutation entropy, which is essentially parameter-free, temporally local, yields straightforward statistical tests, and has fast convergence properties. We apply this method to the study of financial time series, showing that stocks and indices present a rich irreversibility dynamics. We illustrate the comparative methodological advantages of our method with respect to a recently proposed method based on visibility graphs, and discuss the implications of our results for financial data analysis and interpretation.

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Horizontal visibility graphs: Exact results for random time series

Physical Review E ◽

10.1103/physreve.80.046103 ◽

2009 ◽

Vol 80 (4) ◽

Cited By ~ 321

Author(s):

B. Luque ◽

L. Lacasa ◽

F. Ballesteros ◽

J. Luque

Keyword(s):

Time Series ◽

Random Time ◽

Exact Results ◽

Horizontal Visibility ◽

Visibility Graphs

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An empirical comparison of sales time series for online and offline channels for commodities in China

Mathematical Structures in Computer Science ◽

10.1017/s0960129512000503 ◽

2014 ◽

Vol 24 (5) ◽

Author(s):

JINLONG WANG ◽

CAN WEN ◽

XIAOYI WANG

Keyword(s):

Time Series ◽

Complex Networks ◽

Power Law ◽

Constant Parameter ◽

Power Law Distribution ◽

Empirical Comparison ◽

Visibility Graphs ◽

Offline Channels ◽

Power Law Distributions

In this paper we make an empirical comparison of sales time series for online and offline channels. In particular, we analyse the sales dynamic and fluctuation level underlying the sales time series in different channels. The accumulative daily sales distributions of commodities are analysed statistically and the daily sales series are also studied from the perspective of complex networks. We find that most of the commodities' accumulative sales distributions can be fitted by power-law distributions. Visibility graphs are constructed for the daily sales series, and the accumulative degree distributions are also investigated – it is found that they also almost follow power-law distribution. The constant parameter α indicates that different specifications of the same goods have different sales characteristics, and different forms of packaging of commodities, either special offer or ordinary, also show distinctive sales fluctuation levels. The differences show that the direction of these relationships is opposite for online and offline channels.

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Multifractal analysis of solar flare indices and their horizontal visibility graphs

Nonlinear Processes in Geophysics ◽

10.5194/npg-19-657-2012 ◽

2012 ◽

Vol 19 (6) ◽

pp. 657-665 ◽

Cited By ~ 12

Author(s):

Z. G. Yu ◽

V. Anh ◽

R. Eastes ◽

D.-L. Wang

Keyword(s):

Time Series ◽

Solar Cycle ◽

Detrended Fluctuation Analysis ◽

Multifractal Analysis ◽

Fluctuation Analysis ◽

Horizontal Visibility ◽

Multifractal Detrended Fluctuation Analysis ◽

X Ray ◽

Visibility Graphs ◽

Detrended Fluctuation

Abstract. The multifractal properties of the daily solar X-ray brightness, Xl and Xs, during the period from 1 January 1986 to 31 December 2007 which includes two solar cycles are examined using the universal multifractal approach and multifractal detrended fluctuation analysis. Then we convert these time series into networks using the horizontal visibility graph technique. Multifractal analysis of the resulting networks is performed using an algorithm proposed by us. The results from the multifractal analysis show that multifractality exists in both raw daily time series of X-ray brightness and their horizontal visibility graphs. It is also found that the empirical K(q) curves of raw time series can be fitted by the universal multifractal model. The numerical results on the raw data show that the Solar Cycle 23 is weaker than the Solar Cycle 22 in multifractality. The values of h(2) from multifractal detrended fluctuation analysis for these time series indicate that they are stationary and persistent, and the correlations in the time series of Solar Cycle 23 are stronger than those for Solar Cycle 22. Furthermore, the multifractal scaling for the networks of the time series can reflect some properties which cannot be picked up by using the same analysis on the original time series. This suggests a potentially useful method to explore geophysical data.

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