[Paper Review] Inference for High-Dimensional Local Projection

Jiti Gao, FEI LIU+1 more|arXiv (Cornell University)|Feb 11, 2026

Financial Risk and Volatility Modeling0 citations

TL;DR

This paper analyzes local projection in a high-dimensional setting, focusing on robust long-horizon inference and HD covariance estimation under flexible residual dependence. It validates theory with simulations and an empirical study on business news attention and 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.

Motivation & Objective

• Motivate and develop a high-dimensional local projection framework for long-horizon forecasting.
• Incorporate a flexible residual structure to capture general dependence in forecasting models.
• Study high-dimensional covariance estimation challenges specific to long-horizon LP settings.
• Provide theoretical results supplemented by Monte Carlo simulations.
• Demonstrate the framework with an empirical application to financial data.

Proposed method

• Adopt a high-dimensional local projection setup with a flexible residual specification to capture dependence across horizons.
• Derive theoretical properties for inference under the HD setting and long-horizon scope.
• Address the estimation complexity of the HD covariance matrix in long-horizon LP.
• Use extensive Monte Carlo simulations to validate theoretical results.
• Apply the HD LP framework to analyze the impact of business news attention on industry-level stock volatility.

Experimental results

Research questions

• RQ1 How does local projection perform in high-dimensional settings for long-horizon forecasts?
• RQ2 What are the theoretical properties of inference under flexible residual dependence in HD LP?
• RQ3 How can one accurately estimate the covariance matrix in high dimensions with long horizons?
• RQ4 Do Monte Carlo simulations corroborate the theoretical findings in HD LP?
• RQ5 What is the empirical impact of business news attention on U.S. industry-level stock volatility within the HD LP framework?

Key findings

• The HD LP framework yields rigorous inference results under a general dependence structure for residuals.
• The paper addresses the complexity of HD covariance estimation in long-horizon contexts.
• Monte Carlo simulations substantiate the theoretical properties of the proposed method.
• Empirical analysis demonstrates the framework's applicability to measuring business news attention effects on stock volatility.