Complex network analysis of time series

Abstract

Data in the form of time series are ubiquitous that they can be found everywhere and the analysis of time series has long been important for extracting meaningful statistics and valuable information of systems in a variety of research fields. Although time series and complex networks share many relevant applications, the bridge between time series and complex network did not appear until 2006 when a method of transforming pseudoperiodic time series into the so-called cycle networks was introduced. Transforming time series into complex networks enables understanding of the correlation structure and dynamical properties of the time series by using the graph and network theory. This thesis presents a novel framework by using complex networks to represent phase space dynamics from time series. The construction of recurrence networks by the ε-networks method and the k-nearest neighbor networks method is studied. Although a complete study for ε recurrence networks has been reported previously, no complete study of the theoretical foundation underlying the k-nearest neighbor approach has been provided. This thesis specifically addresses this deficiency. The key contributions of this thesis include: 1. a critical review of the network-based time series analysis methods; 2. an extension of the study of the k-nearest neighbor networks from the motif patterns to the full gamut of statistics which describe the time series at different scales; 3. an exposition of the origin of motif properties for k-nearest neighbor networks and links from the network properties to the topology of the time series; and 4. a detailed comparison between the k-nearest neighbor network method and the ε-recurrence network method, the result from which would provide insights to proper parameter selection when using these two methods. The results from this work offer new theoretical insights into the application of complex network theory in time series analysis, and provide novel analytical perspectives of time series problems from a complex network viewpoint.