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arXiv · 2403.13340

Forecasting density-valued functional panel data

Cristian F. Jiménez-Varón·Ying Sun·Han Lin Shang
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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 $h$-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.

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Cristian F. Jiménez-Varón, Ying Sun, Han Lin Shang. 2024-03-20. Forecasting density-valued functional panel data. https://arxiv.org/abs/2403.13340

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