21/09/2026
๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐๐๐ | Advancing Statistical Modeling Through Optimal Transport and Functional Time Series Analysis
As data become increasingly complex and dynamic, understanding how patterns and relationships evolve over time is important for improving statistical analysis and prediction. Functional time series provide a framework for analyzing data that are observed continuously or in complex forms, but their nonstationary nature presents challenges in accurately estimating conditional distributions and making reliable forecasts.
The study โ๐๐ฉ๐ญ๐ข๐ฆ๐๐ฅ ๐ญ๐ซ๐๐ง๐ฌ๐ฉ๐จ๐ซ๐ญ ๐๐จ๐ง๐ฏ๐๐ซ๐ ๐๐ง๐๐ ๐จ๐ ๐๐จ๐ง๐๐ข๐ญ๐ข๐จ๐ง๐๐ฅ ๐๐ข๐ฌ๐ญ๐ซ๐ข๐๐ฎ๐ญ๐ข๐จ๐ง ๐๐ฌ๐ญ๐ข๐ฆ๐๐ญ๐ข๐จ๐ง ๐๐จ๐ซ ๐ฌ๐ข๐ง๐ ๐ฅ๐-๐ข๐ง๐๐๐ฑ๐๐ ๐ฅ๐จ๐๐๐ฅ๐ฅ๐ฒ ๐ฌ๐ญ๐๐ญ๐ข๐จ๐ง๐๐ซ๐ฒ ๐๐ฎ๐ง๐๐ญ๐ข๐จ๐ง๐๐ฅ ๐ญ๐ข๐ฆ๐ ๐ฌ๐๐ซ๐ข๐๐ฌโ develops a statistical methodology for estimating conditional distributions in locally stationary functional time series using a functional single-index model and optimal transport techniques.
The researchers introduce a NadarayaโWatson kernel estimator that simultaneously accounts for temporal variation and a data-driven single index. Using the 1-Wasserstein distance, the framework establishes uniform convergence rates while accounting for weak dependence and the complex structure of functional data. The methodology also provides a practical procedure for estimating the single index and bandwidth through cross-validation.
Extensive simulation results support the theoretical convergence behavior of the proposed approach. Applications to financial and physiological time series further demonstrate its usefulness for distributional forecasting, while an electricity price case study illustrates its potential for predictive analysis in complex nonstationary environments.
Authors:
๐๐๐ง ๐๐ข๐ง๐จ ๐. ๐๐ข๐ง๐ข๐จ
๐๐จ๐ค๐ก๐ญ๐๐ซ ๐. ๐๐ฅ๐๐ฒ๐
๐๐๐ฅ๐ข๐ฆ ๐๐จ๐ฎ๐ณ๐๐๐๐
Journal:
๐๐๐ฌ๐ฎ๐ฅ๐ญ๐ฌ ๐ข๐ง ๐๐ฉ๐ฉ๐ฅ๐ข๐๐ ๐๐๐ญ๐ก๐๐ฆ๐๐ญ๐ข๐๐ฌ
๐๐จ๐ฅ๐ฎ๐ฆ๐ ๐๐ (๐๐๐๐), ๐๐ซ๐ญ๐ข๐๐ฅ๐ ๐๐๐๐๐๐
Publisher:
๐๐ฅ๐ฌ๐๐ฏ๐ข๐๐ซ ๐.๐.
Indexed:
๐๐๐จ๐ฉ๐ฎ๐ฌ; ๐๐๐ ๐จ๐ ๐๐๐ข๐๐ง๐๐ (๐๐๐๐); ๐๐ข๐ซ๐๐๐ญ๐จ๐ซ๐ฒ ๐จ๐ ๐๐ฉ๐๐ง ๐๐๐๐๐ฌ๐ฌ ๐๐จ๐ฎ๐ซ๐ง๐๐ฅ๐ฌ (๐๐๐๐)
Read more: https://doi.org/10.1016/j.rinam.2026.100709