Analysis of Distributional Dynamics for Repeated Cross-Sectional and Intra-Period Observations
This paper addresses the challenge of modeling the dynamic evolution of state density functions in two distinct data structures: repeated cross-sections (e.g., monthly stock return distributions) and high-frequency intra-period time series (e.g., intraday GBP/USD return distributions). We propose the first unified functional dynamic framework compatible with both. Methodologically, we embed density functions into a Hilbert space and formulate a functional autoregressive (FAR) model, integrating kernel density estimation with asymptotic statistical inference. Theoretically, we establish asymptotic theory for density forecasting and distributional moment dynamics, and prove strong consistency of the estimators. Empirically, our approach significantly outperforms conventional methods on GBP/USD and NYSE datasets, delivering high-accuracy density forecasts. The core innovation lies in overcoming data-type barriers—enabling, for the first time, unified modeling and theoretical analysis of distributional evolution across both inter-period cross-sectional and intra-period temporal dimensions.