标题： 基于混合频率数据的收入分布密度预测 显示英文标题

标题： Density Prediction of Income Distribution Based on Mixed Frequency Data

摘要： 在现代时间序列分析中，对大型相关数据集进行建模是一个关键的研究领域。 处理此类数据集的一种有效方法是将观测值转换为密度函数，并应用统计方法进行进一步分析。 收入分布预测是一种常见的应用场景，通过预测密度函数可以考虑点估计周围的不确定性，从而制定更明智的政策。 然而，当处理混合频率数据时，预测建模变得具有挑战性。 为了解决这一挑战，本文引入了一种用于概率密度函数（PDF-MIDAS）的混合数据抽样回归模型。 为了减轻高频预测变量引起的方差膨胀，我们利用参数较少的指数阿尔蒙多项式来规范系数结构。 此外，我们提出了一种基于二次规划和BFGS算法的迭代估计方法。 模拟分析表明，随着估计密度函数的样本量和观测长度增加，估计量会趋近于真实值。 实际数据分析表明，与单序列预测模型相比，包含高频外生变量的PDF-MIDAS在应用范围、拟合和预测性能方面表现更优。 显示英文摘要

摘要： Modeling large dependent datasets in modern time series analysis is a crucial research area. One effective approach to handle such datasets is to transform the observations into density functions and apply statistical methods for further analysis. Income distribution forecasting, a common application scenario, benefits from predicting density functions as it accounts for uncertainty around point estimates, leading to more informed policy formulation. However, predictive modeling becomes challenging when dealing with mixed-frequency data. To address this challenge, this paper introduces a mixed data sampling regression model for probability density functions (PDF-MIDAS). To mitigate variance inflation caused by high-frequency prediction variables, we utilize exponential Almon polynomials with fewer parameters to regularize the coefficient structure. Additionally, we propose an iterative estimation method based on quadratic programming and the BFGS algorithm. Simulation analyses demonstrate that as the sample size for estimating density functions and observation length increase, the estimator approaches the true value. Real data analysis reveals that compared to single-sequence prediction models, PDF-MIDAS incorporating high-frequency exogenous variables offers a wider range of application scenarios with superior fitting and prediction performance.