Forecasting density-valued functional panel data
Abstract
We introduce a statistical method for modeling and forecasting functional panel data represented by multiple densities. Density functions are nonnegative and have a constrained integral and thus do not constitute a linear vector space. We implement a center log-ratio transformation to transform densities into unconstrained functions. These functions exhibit cross-sectional correlation and temporal dependence. Via a functional analysis of variance decomposition, we decompose the unconstrained functional panel data into a deterministic trend component and a time-varying residual component. To produce forecasts for the time-varying component, a functional time series forecasting method, based on the estimation of the long-run covariance, is implemented. By combining the forecasts of the time-varying residual component with the deterministic trend component, we obtain -step-ahead forecast curves for multiple populations. Illustrated by age- and sex-specific life-table death counts in the United States, we apply our proposed method to generate forecasts of the life-table death counts for 51 states.
Cite
@article{arxiv.2403.13340,
title = {Forecasting density-valued functional panel data},
author = {Cristian F. Jiménez-Varón and Ying Sun and Han Lin Shang},
journal= {arXiv preprint arXiv:2403.13340},
year = {2025}
}