Inference for High-Dimensional Local Projection

2026-02-11

AI Summary

This study addresses the challenge of conducting robust long-horizon inference in high-dimensional settings, where local projection methods are hindered by complex residual dependence structures and difficulties in covariance estimation. The paper proposes a novel integration of high-dimensional local projections with h-step-ahead forecasting, introducing a flexible approach to modeling residual dependencies that enables consistent covariance estimation tailored for long-horizon analyses. The method is accompanied by rigorous theoretical guarantees, which are corroborated through Monte Carlo simulations. In an empirical application, the framework reveals the dynamic impact of business news attention on U.S. industry-level stock return volatility, thereby demonstrating its practical relevance and methodological innovation.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Kernel Methods
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Social networks and social learning

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.

Problem

• high-dimensional
• local projection
• long-horizon inference
• covariance matrix estimation
• dependence structure

Innovation

• High-Dimensional Local Projection
• Long-Horizon Inference
• Dependence Structure
• Covariance Matrix Estimation
• Robust Forecasting