Information–Theoretic Analysis of Visibility Graph Properties of Extremes in Time Series Generated by a Nonlinear Langevin Equation

In this study, we examined how the nonlinearity α of the Langevin equation infl uences the behavior of extremes in a generated time series. The extremes, defi ned according to run theory, result in two types of series, run lengths and surplus magnitudes, whose complex structure was investigated using the visibility graph (VG) method. For both types of series, the information measures of the Shannon entropy measure and Fisher Information Measure were utilized for illustrating the infl uence of the nonlinearity α on the distribution of the degree, which is the main topological parameter describing the graph constructed by the VG method. The main fi nding of our study was that the Shannon entropy of the degree of the run lengths and the surplus magnitudes of the extremes is mostly infl uenced by the nonlinearity, which decreases with with an increase in α. This result suggests that the run lengths and surplus magnitudes of extremes are characterized by a sort of order that increases with increases in nonlinearity.