Relation Between Autocorrelation Sequence and Average Shortest-Path Length in a Time Serie to Network Mapping

Amanda Leite de Camargo; Marcio Eisencraft

Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Relation Between Autocorrelation Sequence and Average Shortest-Path Length in a Time Serie to Network Mapping

Discontinuity, Nonlinearity, and Complexity 8(2) (2019) 241--246 | DOI:10.5890/DNC.2019.06.010

Amanda Leite de Camargo, Marcio Eisencraft

Universidade Federal do ABC, Santo André, Brazil and Escola Polit´ecnica, University of São Paulo, São Paulo, Brazil

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Abstract

An invertible mapping between time series and networks was recently proposed. It can be used as a tool to figure out properties of the mapped time series. In the present work we use controlled artificial signals to numerically investigate how correlation properties of time series are mapped in the topological measures of associated networks. More specifically, we employ filtered uniform white noise and analyse how the autocorrelation sequence influences the average shortest-path length.

Acknowledgments

This study was financed in part by the Coordenação de Aperfeic¸oamento de Pessoal de Nível Superior - Brazil (CAPES) - Finance Code 001. M.E. was partially supported by CNPq (grant 309275/2016-4).

References

[1] Campanharo, A.S.L.O., Sirer, M.I., Malmgren, R.D., Ramos, F.M., and Amaral, L.A.N. (2011), Duality between time series and networks, PLoS ONE, 6, p. e23378.
[2] Zhang, J. and Small, M. (2006), Complex network from pseudoperiodic time series: Topology versus dynamics, Physical Review Letters, 96, p. 238701.
[3] Luque, B., Lacasa, L., Ballesteros, F., and Luque, J. (2009), Horizontal visibility graphs: Exact results for random time series, Physical Review E, 80.
[4] Baggio, R. and Sainaghi, R. (2016), Mapping time series into networks as a tool to assess the complex dynamics of tourism systems Tourism Management, 54, 23-33.
[5] West, D.B. (2000), Introduction to Graph Theory, Prentice Hall.
[6] Boccaletti, S., Latora, V.,Moreno, Y., Chavez, M., and Hwang, D. (2006), Complex networks: Structure and dynamics, Physics Reports, 424, 175-308.
[7] Monteiro, L. (2014), H.A. Sistemas Dinâmicos Complexos (in Brazilian Portuguese). Livraria da Física, 2a ed..
[8] Oppenheim, A.V. and Schafer, R.W. Discrete-Time Signal Processing, Upper Saddle River, NJ, USA: AddisonWesley Pub Co Inc, 3rd ed., 2009.
[9] Peebles, P. (2000), Probability, Random Variables, and Random Signal Principles. McGraw-Hill Science/Engineering/Math.