Density prediction of income distribution based on mixed frequency data

With the continuous deepening of economic system reforms across countries, increasing household income and improving income distribution systems have received growing attention. To achieve effective economic development, countries must broaden their perspective, shifting from a sole focus on the ‘mean’ of income to considering the entire income ‘distribution’. Therefore, research on predicting the density functions of household income distribution holds significant practical importance. However, when modelling and predicting density functions, one encounters the challenge of inconsistent observation frequencies among indicators. To address this challenge, this paper extends the structure of the mixed data sampling (MIDAS) regression to probability density functions and proposes a mixed data sampling regression model for probability density functions (PDF-MIDAS). To reduce the number of parameters to be estimated for high-frequency predictors, we employ parsimonious exponential Almon polynomials to regularize the coefficient structure. Additionally, we propose an iterative estimation method to estimate the model parameters. Simulation analyses demonstrate that as the sample size for estimating density functions and the observation length increase, the root mean square error (RMSE) of the estimator decreases progressively. Real data analysis demonstrates that the proposed PDF-MIDAS model exhibits superior performance in predicting the density functions of household income distribution.