Density Prediction of Income Distribution Based on Mixed Frequency Data

TL;DR

This paper introduces a novel mixed-frequency regression model for predicting income distribution densities, improving accuracy and applicability by regularizing high-frequency variables and using iterative estimation methods.

Contribution

The paper develops PDF-MIDAS, a new approach for density prediction with mixed-frequency data, incorporating regularization and iterative estimation techniques.

Findings

Simulation shows estimator approaches true density with larger samples.

Real data analysis confirms superior performance over single-sequence models.

Model provides wider application scenarios with better fit and prediction.

Abstract

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.