# Granger Causality Testing in High-Dimensional VARs: a Post-Double-Selection Procedure

## TL;DR

This paper introduces a new Granger causality test for high-dimensional VAR models using a post-double-selection approach with penalized least squares, validated through simulations and applied to volatility spillover networks.

## Contribution

It proposes a novel LM test for high-dimensional VARs that remains valid after variable selection, addressing a key challenge in high-dimensional time series analysis.

## Key findings

- Test performs well across various data generating processes
- Causal relationships are clearer in high-dimensional models
- Method is effective even without sparsity assumptions

## Abstract

We develop an LM test for Granger causality in high-dimensional VAR models based on penalized least squares estimations. To obtain a test retaining the appropriate size after the variable selection done by the lasso, we propose a post-double-selection procedure to partial out effects of nuisance variables and establish its uniform asymptotic validity. We conduct an extensive set of Monte-Carlo simulations that show our tests perform well under different data generating processes, even without sparsity. We apply our testing procedure to find networks of volatility spillovers and we find evidence that causal relationships become clearer in high-dimensional compared to standard low-dimensional VARs.