Exploration of stationary time-series’ network properties : Visibility-and Horizontal visibility graph of Gaussian white noise, AR (1), MA (1) and ARMA (1,1)

Abstract

We haverecordedthe network properties ofstochastic processes’whitenoise,푀퐴(1), 퐴푅(1)and 퐴푅푀퐴(1,1)bymeansof visibility-and horizontal visibility algorithms. The sample series of the stochastic processeswere artificially generated and used in simulationswith multiple repetitions. We examined six global network properties:mean degree, normalized degree centrality, degree distribution, transitivity, assortativity and average geodesic pathtodiscover how theyreflect the structure of the series. These properties were also used to disclose change in behavior due to variation in the series length.Our contribution to the literature isathorough recordingofbasic stochastic processes’ network statistics, andthe interpretation of these related to time-series.To our knowledge, this is the first time a documentationof this magnitude has been attempted. The thesis result will disclose that the combined network statistics mentioned above are able to recognize a Gaussian white noise process, both by visibility-and horizontal visibility graphs. It is, in addition, possible to distinguish between the processes different autocorrelation coefficients by means of the visibility graph.