Consistent Variable Selection for GARCH-X Models

TL;DR

This paper introduces a consistent variable selection method for GARCH-X models using multiple hypothesis testing and FDR control, validated through simulations and applied to SP 500 volatility modeling.

Contribution

It proposes a novel variable selection procedure for GARCH-X models that guarantees asymptotic consistency and robustness.

Findings

The method accurately identifies relevant covariates in simulations.

It asymptotically recovers the true set of variables as sample size grows.

Applied to SP 500 data, it effectively selects macroeconomic and commodity indicators.

Abstract

In this paper we develop a consistent variable selection procedure for GARCH-X models that identifies the truly relevant exogenous covariates influencing volatility dynamics. The proposed method is based on a multiple hypothesis testing framework with Wald-type test statistics and the Benjamini-Yekutieli False Discovery Rate (FDR) procedure to control the proportion of false discoveries. We establish the consistency of the selection rule, showing that it asymptotically recovers the correct set of covariates as the sample size increases. Monte Carlo simulations across different distributions and dependence structures validate the method's accuracy and robustness. The procedure is applied to modeling the volatility of the SP 500 using macroeconomic and commodity indicators.