Inference for High-Dimensional Local Projection

TL;DR

This paper develops a high-dimensional local projection framework for robust long-horizon inference, incorporating dependence structures and covariance estimation, validated through simulations and applied to stock volatility analysis.

Contribution

It introduces a novel high-dimensional local projection methodology with dependence modeling and covariance estimation for long-horizon inference.

Findings

Theoretical properties of HD LP are established.

Simulation results support the theoretical findings.

Empirical application reveals insights into stock volatility.

Abstract

This paper rigorously analyzes the properties of the local projection (LP) methodology within a high-dimensional (HD) framework, with a central focus on achieving robust long-horizon inference. We integrate a general dependence structure into h-step ahead forecasting models via a flexible specification of the residual terms. Additionally, we study the corresponding HD covariance matrix estimation, explicitly addressing the complexity arising from the long-horizon setting. Extensive Monte Carlo simulations are conducted to substantiate the derived theoretical findings. In the empirical study, we utilize the proposed HD LP framework to study the impact of business news attention on U.S. industry-level stock volatility.