Forecasting density-valued functional panel data
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912222783995904 |
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| author | Jiménez-Varón, Cristian F. Sun, Ying Shang, Han Lin |
| author_facet | Jiménez-Varón, Cristian F. Sun, Ying Shang, Han Lin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Forecasting density-valued functional panel data Jiménez-Varón, Cristian F. Sun, Ying Shang, Han Lin Methodology 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. |
| title | Forecasting density-valued functional panel data |
| topic | Methodology |
| url | https://arxiv.org/abs/2403.13340 |