We introduce a statistical method for modeling and forecasting functional panel data, where each element is a density. 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-sectionally 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-range 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.

翻译：本文提出一种用于建模和预测函数型面板数据的统计方法，其中每个元素均为密度函数。由于密度函数具有非负性和积分约束条件，无法构成线性向量空间。我们采用中心化对数比变换将密度函数转化为无约束函数，这些函数同时呈现截面相关性和时间依赖性。通过函数型方差分析分解，我们将无约束函数型面板数据分解为确定性趋势分量和时变残差分量。针对时变分量预测，基于长程协方差估计的函数型时间序列预测方法得以实施。通过将时变残差分量的预测值与确定性趋势分量相结合，可获得多总体h步超前预测曲线。以美国按年龄和性别分列的生命表死亡人数为例，我们将所提方法应用于50个州及哥伦比亚特区的生命表死亡人数预测生成。