New Frontiers in Time Series Analysis

Big data are now prevalent in nearly every domain. While shrinkage and sparse estimators are essential to mitigate the volume issues posed by big datasets, innovative models are needed to address their variety and velocity demands. Indeed, enhanced monitoring and measurement systems now provide data at high enough resolutions that observations can often be considered intrinsically continuous or functional.

Massive environmental, biological, industrial, and computational networks are being dynamically recorded such that their intricate evolution might be succinctly monitored, studied, and maintained. Vast datasets are generated every day, ranging from large-scale satellites and remote sensing instruments, emergency systems, and energy infrastructure, to nanoscale electromagnetic sensors, medical devices, and imaging devices.

These systems provide rich information about our human-natural world, and most is sequential, or time-ordered and exhibit complex trends, transitions, and dependencies. Standard methods in multivariate statistics are unsuitable and insufficiently adaptable. The Principal Investigator (PI) will develop new methods and computational tools to aid data-driven scientific discovery and industry applications.

The PI will also train and mentor graduate and undergraduate student research, freely disseminate new software and methodology across application areas, and foster collaboration between statistics and a wide range of fields, including economics, ecology, physics, finance, space weather, hydrology, agriculture, energy, environmental engineering, biophysics, mathematics, electrical engineering, human development, and computer science.

Most time-indexed data exhibit heteroskedastic noise, anomalies, change points, local and global trends, and both linear and nonlinear dependence, and there is a striking shortage of analytical tools suitable for modeling such complexity. Shrinkage, sparse, and adaptive estimators are exceptions and have become vital tools. Global-local and regularized estimation, via adaptive sparsity/smoothness-inducing penalties/priors, is essential — it allows computationally tractable estimation of complex models, with greater interpretability and reduced estimation uncertainty.

The PI will develop: (i) new methods and computational frameworks for change-point detection with increased flexibility by allowing global and segment-specific parameters; (ii) new theoretical and application-driven investigations into less explored aspects of hidden Markov models; (iii) extensions of dynamic shrinkage process for robust and adaptive estimation of change-points in the presence of outliers, spillover effects and causal inference on dependent network time series, and distributional trend filtering; (iv) new methods for simultaneous modeling and inference of dynamic functional data with complex features such as long range dependence and stochastic volatility.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.