Visual analysis of periodic time series data : supporting model selection, prediction, imputation, and outlier detection using visual analytics

Abstract

Time series data are essential in many fields, like economics, natural sciences, and medicine, to name a few. Measuring and recording these data allow us to document, analyze, and make decisions. One of the most natural structures in time series across all areas is periodicity, which stems from either the natural phenomena measured or the underlying calendar structure. One finds the structural property of time in many of these time series by periodic reoccurrences. In a time series analysis, these properties are mostly beneficial, if identified correctly and modeled adequately, for tasks like model selection, prediction, imputation, and outlier detection. These periodic patterns can be obvious due to the context or hidden in the data itself. Visualization is one way for human perception to identify such patterns easily and allow for the exploration, identification, and investigation of such underlying patterns using visual analysis. In this dissertation, we consider the different stages of time series analysis for periodic time series, starting with exploring the time series, selecting appropriate time series models, supporting the parametrization, examining the prediction performance, imputing missing values, and detecting outliers. For all these steps, we investigate how Visual Analytics can support users in these tasks and how intertwining new perspectives on periodic time series using visualization together with user perception, interaction techniques, and statistical computations fosters the user in analyzing periodic time series. We first propose a Visual Analytics approach for supporting the whole process of selecting appropriate time series models, allowing the visual exploration of time series while guiding the model selection, parametrization, and model diagnostics. We then investigate how to integrate the prediction capabilities of the model into the model selection process. Next, we employ a cycle plot representation to support the imputation of missing values in periodic time series. Thereafter, we present a novel abstraction method to use a cycle plot representation for multivariate time series as well in order to use it for outlier detection in periodic time series. For each of the proposed solutions, we employed an iterative user-centered design process; we showed the utility of the approaches in usage scenarios and thoroughly illustrated walk-throughs. Furthermore, we discussed the implications of such methods and concluded with open challenges in these topics. Integrating additional focus on visualizing periodicity into the Visual Analytics approaches allows for better comprehending the applied models, predictions, imputations, and outliers. The results indicate that adequate visual representation and abstraction, when considering the periodic structure of time, allows for the analysis of time series from different perspectives and provides possibilities for identifying adequate time series models, supporting the imputation of missing values, and identifying outliers.