Data analysis has been motivating new methods to find patterns, clusters and outliers in different scenarios and conditions. In the scope of data evolving along time, also referred to as time series or data streams, solutions derived from areas such as Dynamical Systems and Statistics (DSS) have gained special attention in the literature. However, the DSS framework is usually not applied/combined with other areas in the given context. Based on this drawback, we propose an exploratory method with supporting techniques to analyze time series combining DSS approaches with Visualization metaphors to answer typical questions related to time-dependent data in a more effective and efficient way. More than having a user-friendly application providing interactive exploration, we understand Visualization adds value to DSS by revealing additional data information. With our proposed method, namely Visual DSS (VDSS), one could determine a series nature (deterministic, chaotic, stationary, etc.), forecast never seen observations, and proceed with classification. More precisely, this project has three lines of research. First, we intend to improve how one can visually explore time series similarities and attributes. In order to do that, we consider an hierarchical-bundle metaphor based on the Cross-Recurrence Quantification Analysis. Second, we correlate phase-spaces and time-series attributes through the usage of Multidimensional Projections, RadViz and Parallel Coordinates metaphors. Finally, we investigate how much dimensionality reduction impacts forecasting accuracy after applying Takens' embedding theorem.
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