Analysis of Distributional Dynamics for Repeated Cross-Sectional and Intra-Period Observations

TL;DR

This paper develops a new functional autoregressive model to analyze the dynamics of state distributions in high-frequency and cross-sectional financial data, providing tools for density forecasting and distributional analysis.

Contribution

It introduces a novel estimator for the functional autoregressive operator and establishes its consistency, enabling analysis of distributional dynamics in complex financial datasets.

Findings

Effective density forecast tools demonstrated on exchange rate data.

Model captures intra-month and cross-sectional distributional changes.

Simulation results validate the forecasting approach.

Abstract

This paper introduces a novel approach to investigate the dynamics of state distributions, which accommodate both cross-sectional distributions of repeated panels and intra-period distributions of a time series observed at high frequency. In our approach, densities of the state distributions are regarded as functional elements in a Hilbert space, and are assumed to follow a functional autoregressive model. We propose an estimator for the autoregressive operator, establish its consistency, and provide tools and asymptotics to analyze the forecast of state density and the moment dynamics of state distributions. We apply our methodology to study the time series of distributions of the GBP/USD exchange rate intra-month returns and the time series of cross-sectional distributions of the NYSE stocks monthly returns. Finally, we conduct simulations to evaluate the density forecasts based on our model.