Time Series Analysis based on Complex Networks

Time series data are ubiquitous in domains as diverse as climate studies, economics and health care. Mining interesting features from these data is therefore a crucial task with an inherent multidisciplinary impact. Time series analysis is a well established research field with a vast array of available methodologies. Due to recent technological advances, ranging from remote sensing to wearables and social sensing, there is a tremendous increase in time series data that is available and requires analysis. Complex networks can also describe a wide range of systems in nature and society and their analysis has been receiving increasing interest from the research community. The impact has been so big that has led to the emergence of the new field of Network Science, and there exists a vast set of topological graph measurements available, an established set of problems and a large track record of successful applications. At first sight, time series and complex networks do not seem to be related, but there have been recent advances that try to leverage the knowledge of both worlds. The classical approaches to time series analysis present severe limitations when analysing multidimensional sets of time series. A recent and very promising conceptual approach relies on mapping the time series to complex networks, where the vast arsenal of network science methodologies can help to gain new insights into the mapped time series. This thesis main goal focuses precisely on contributing to time series analysis based on complex networks. We first give an overview the main concepts of both areas and we survey the literature on mappings that able to transform time series into complex networks that preserve some of its characteristics. These mappings are based on concepts such as correlation, phase space reconstruction, recurrence analysis, visibility or transition probabilities. We then perform a systematic network based characterization of a large set of linear and nonlinear time series models using topological properties of the constructed networks using the visibility and transition probabilities concepts. We show that different mappings and different topological metrics capture different characteristics, complementing each other and providing more information when combined than simply being considered by themselves.

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