Leaps-MPS: novel dependence metrics in spectral analysis for modern time series data

The National Science Foundation's Directorate for Mathematical and Physical Sciences (Mathematical and Physical Sciences program, CFDA 47.049) awarded $246,755 to the Research Foundation of the City University of New York (RFCUNY), operating as Rfcuny - Baruch College, effective September 15, 2025, with completion targeted for August 31, 2027. This Project Grant funds research to develop novel spectral dependence metrics capable of analyzing complex, modern time series data across functional, tensor, and high-dimensional forms. The research will establish robust frequency detection and signal processing methodologies through dimension reduction techniques that extend beyond traditional covariance-based approaches, enabling the capture of both linear and nonlinear temporal dependence patterns in large-scale datasets.

The project delivers advanced statistical tools and computational methods designed to extract hidden signals from sophisticated time series data generated across biomedicine, economics, and financial systems. By creating more powerful analytical capabilities, the research supports improved medical diagnoses, economic policy decisions, and financial market stability assessment. The initiative also emphasizes cross-disciplinary partnerships and educational components, making these modern time series methodologies and computational tools accessible to researchers across multiple STEM fields while enhancing workforce development and educational opportunities in data science and statistical modeling.

Abstract

Vast volumes of modern time series data emerge from advances in technologies and computational capabilities across various fields such as biomedicine, economics, and financial systems. These data hold critical information for improving human health, economic stability, and national prosperity. However, current analysis methods, designed for simpler data types, fail to extract the full range of patterns and signals embedded in these sophisticated datasets. This limitation restricts our ability to detect early disease markers, predict economic trends, or identify financial risks. This project will develop advanced statistical tools capable of analyzing complex modern time series data to uncover hidden signals that could lead to better medical diagnoses, economic patterns that inform policy decisions, and financial indicators that enhance market stability. By creating more powerful and flexible analytical methods, this research directly supports NSF's mission to advance national health, prosperity, and welfare through scientific progress, while also providing new computational tools that will benefit researchers across multiple disciplines and enhance educational opportunities in data science and statistical modeling. Additionally, this project will foster cross-disciplinary partnerships between stem fields, economics, and finance, making the modern time series methodologies and computational tools accessible to a broad range of research communities. The project aims to develop novel spectral dependence metrics that comprehensively capture general dynamics, including both linear and nonlinear temporal dependence, in modern time series data? Functional, tensor, and high-dimensional forms. The research will establish robust frequency detection, signal processing through dimension reduction built upon these new spectral dependence metrics, extending beyond traditional covariance-based spectral density approaches that capture only linear relationships. Since linear dependence inadequately summarizes complete dynamics in non-gaussian data, the proposed approaches offer enhanced flexibility regarding both dependence structures and distributional assumptions. In particular, this project will focus on: (1) developing robust spectral dependence metrics with rigorous theoretical properties; (2) flexible frequency pattern detection and signal estimation via dimension reduction procedures for modern time series that can detect underlying biological, economic, and financial signals; and (3) comprehensive software implementations that are simple to use and computationally efficient. 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.- subawards are not planned for this award.