High-Dimensional Functional Time Series Regression Models with Supervised Factor Structures: Theory and Applications

Against the backdrop of intensifying global climate change and the "Healthy China"
strategy, the impact of extreme climate on residents' health and medical insurance
expenditures has become increasingly prominent. Focusing on this critical
real-world issue, this project aims to construct a unified regression analysis
framework for high-dimensional functional time series. First, to address complex
data that are asymptotically infinite simultaneously across cross-sectional,
temporal, and curve dimensions, the project introduces a supervised factor
structure to achieve effective dimensionality reduction, and proposes an effective
estimation method for regression parameters by incorporating canonical correlation
analysis. Second, to tackle data quality issues such as distribution shifts in
medical insurance big data, this project further integrates the idea of
distributionally robust optimization into the model construction and inference
processes, ensuring the robustness of estimation and prediction. Furthermore,
within the high-dimensional functional time series framework, deep neural networks
are utilized to characterize complex non-linear factor loadings driven by
high-dimensional observable features, thereby enhancing the model's
interpretability. Finally, the project systematically applies the proposed methods
to the big data of medical insurance expenditures and meteorology, accurately
identifying the heterogeneous shocks of extreme temperatures on medical
expenditures across different cities and all age groups. This research not only
expands the econometric theory of high-dimensional data but also provides a
quantitative basis for health insurance fund risk early warning, medical resource
optimization, and climate adaptation policies.