Efficient Algorithms with Statistical Guarantees for High Dimensional Time Series

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Various industrial and scientific fields are generating high-dimensional time series data. Time series generated by macroeconomic indicators, stock market performance, and sensors in the industrial internet are of huge value to the economy. Time series generated in systems biology and neuroscience can lead to a better understanding of human health and diseases. Classical statistical methods are limited in their ability to deal with high-dimensional time series. Developing statistical tools for the analysis of high-dimensional time series is thus of pressing concern to society. This project develops both theory as well as scalable algorithms for advancing our ability to analyze and extract meaningful information from high-dimensional time series data.This project will expand the frontier of research at the interface between three areas: high-dimensional statistics, large-scale optimization, and time series analysis. Three interrelated research aims will be pursued. First, theoretical tools to analyze the performance of linear prediction methods for high-dimensional time series under mild assumptions about the generative process underlying the time series will be built. Second, statistical guarantees for computationally efficient alternating minimization based alternatives to computing the maximum likelihood estimator for high-dimensional vector autoregressive (VAR) models will be provided. Third, fast online algorithms for estimation and forecasting in a setting where the high-dimensional time series observations arrive sequentially will be developed.