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 deve