Correlation networks from random walk time series

Abstract

Stimulated by the growing interest in the applications of complex networks framework on time series analysis, we devise a network model in which each of $N$ nodes is associated with a random walk of length $L$. Connectivity between any two nodes is established when the Pearson correlation coefficient(PCC) of the corresponding time series is greater than or equal to a threshold $H$, resulting in similarity networks with interesting properties. In particular, these networks can have high average clustering coefficients, "small world" property, and their degree distribution can vary from scale-free to quasi-constant depending on $H$. A giant component of size $N$ exists until a critical threshold $H_c$ is crossed, at which point relatively rare walks begin to detach from it, and remain isolated. This model can be used as a first step for building a null hypothesis for networks constructed from time series.

9 pages, 11 figures, 2 animations

References in corpus (4)

• Critical phenomena in complex networks
• From time series to complex networks: the visibility graph
• Mean-field transport of a Bose-Einstein condensate
• Scale-free networks emerging from multifractal time series

Cited by in corpus (2)

• Complex-Valued Time Series Based Solar Irradiance Forecast
• Modeling and Analysis of the Lead-Lag Network of Economic Indicators