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.

翻译：本文针对GARCH-X模型提出了一套一致变量选择方法，可识别影响波动率动态的真正相关外生协变量。该方法基于多重假设检验框架，采用Wald型检验统计量与Benjamini-Yekutieli错误发现率控制程序来抑制误发现比例。我们证明了选择规则的一致性，表明随着样本量增大，该方法能渐近地恢复正确的协变量集合。针对不同分布与相依结构的蒙特卡洛模拟验证了该方法的准确性与稳健性。该程序被应用于利用宏观经济与商品指标对标普500指数波动率进行建模。