# Forecasting density-valued functional panel data

arXiv: https://arxiv.org/abs/2403.13340 · HTML: https://mlsanity.com/paper/2403.13340/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Probabilistic Functional Neural Networks](https://mlsanity.com/paper/2503.21585/) (2025)

## Abstract (arXiv)

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 h-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.