This $174,344 federal Project Grant award was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program. The award supports a collaborative research project to develop new statistical models, methodology, and theory for analyzing object-valued time series data common in fields such as finance, healthcare, and materials science. The key products and services to be delivered include: (1) creating an autoregressive model for distributional time series using Wasserstein geometry, along with tools for model estimation, selection, and diagnostics; (2) developing new specification testing procedures for distributional time series in Euclidean space; and (3) creating change-point detection methods to identify distribution shifts in object-valued time series. This research aims to advance the field of object-valued time series analysis by providing a systematic body of innovative methodological and theoretical developments. The project will also involve mentoring a PhD student and engaging undergraduate students. The award period is from January 1, 2025 to June 30, 2027.
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