🤖 AI Summary
This study addresses the challenge of identifying truly relevant exogenous covariates in GARCH-X models for volatility dynamics. The authors propose a variable selection method based on multiple hypothesis testing, which integrates a Wald-type test statistic with the Benjamini–Yekutieli false discovery rate (FDR) control procedure. They establish, for the first time, an asymptotically consistent variable selection rule under the GARCH-X framework that rigorously controls the FDR. Monte Carlo simulations demonstrate that the proposed method exhibits strong accuracy and robustness across various error distributions and dependence structures. Empirical application to S&P 500 index volatility modeling further confirms its practical effectiveness.
📝 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.