CAREER: New Frontiers in Time Series Analysis

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Big data permeates business, engineering, and science -- the number of connected smart devices, even excluding phones, tablets, and PCs, is projected to grow from billions to tens of billions within five years. Vast data is generated from sensors, GPS, RFID, medical devices, and emergency and energy systems, to provide rich information about untold aspects of the modern world. Despite the ubiquity and significant interest in mining such data, there are few existing analytical tools that are suitable. The investigator focuses on the development of new statistical methodology, extending application of these methods to new fields, and on increasing understanding of the theoretical challenges in data-driven model building and inference. The methods under development have the potential to strengthen research in numerous fields, including astronomy, economics, emergency medical services, neuroscience, and statistics itself.Time series analysis is a rich and historic field, but it remains centered on univariate and low dimensional multivariate analysis. In recent years, big data has begun to permeate business, engineering, and science, but despite the ubiquity and significant interest in mining such data, there are few existing analytical tools suitable for data with a time structured format. The investigator studies the development of new high dimensional and functional time series (HDTS) tools to help researchers and practitioners meet increasingly ambitious inferential and modeling aims. Specifically, the investigator studies: (i) new methods for simultaneous modeling, inference, and forecasting of dynamic functional data; (ii) new structured regularization methods for modeling high dimensional time ordered data; (iii) new adaptive, yet methods of stability analysis for big data monitoring systems; and (iv) linking these new methods with emergent lines of inquiry and providing an infrastructure for answering critical research questions in a wide range of fields.