Network Analysis Of Fractional Brownian Motion Time Series Based On Recurrence Plot

Nonlinear time series analysis aims at revealing the dynamics of stochas-tic or chaotic processes. In recent years, many methods including recurrenceplot method have been proposed to convert a single time series to a complexnetwork so that the properties of the original time series can be understood byinvestigating the topological properties of the network. In this paper，we con-vert fractional Brownian motion (FBM) time series to complex networks usingrecurrence plot method, then we investigate the topological properties of the cor-responding recurrence networks. We find that for fixed Hurst exponent H, beforethe connectivity rate of corresponding networks increases to about1for the firsttime, the average length L of the shortest paths increases with the increase of pa-rameter threshold in the recurrence plot, and then decreases. It is also found thatthe converted networks from FBM time series are scale-free. The analysis usingthe node-covering box-counting method shows that the recurrence networks arefractals with self-similarity property, and the fractal dimension dBdecreases withHurst index H, especially when H≥0.4, there is a approximately relationshipdB=H22.1×H+2.