We introduce the ARCH-m(X) model, a semiparametric extension of the ARCH-X framework in which the effect of a multivariate exogenous covariate vector X on the conditional variance is modeled through an unknown nonparametric function m(), accommodating complex nonlinear relationships between external predictors and financial volatility. Within this model, we develop a novel hypothesis test for the significance of covariates constructed with an artificial one-way ANOVA. Under some regularity conditions, the test statistic is shown to converge in distribution to the standard Normal. Another key contribution of this paper is the construction of a variable selection procedure based on the Benjamini-Yekutieli false discovery rate correction applied to covariate-level p-values. We show that the resulting index set coincides with the true set of relevant covariates with probability tending to one as n goes to infinity. Extensive simulations confirm that the proposed methods outperform existing competitors, and an empirical application to SP500 return volatility illustrates the practical utility of the proposed variable selection framework.

翻译：本文提出ARCH-m(X)模型，这是ARCH-X框架的一种半参数扩展。在该模型中，多元外生协变量向量X对条件方差的影响通过未知非参数函数m()进行建模，从而能够刻画外部预测因子与金融波动率之间的复杂非线性关系。基于该模型，我们构建了一种利用人工单因素方差分析的新型协变量显著性假设检验方法。在若干正则性条件下，检验统计量被证明依分布收敛于标准正态分布。本文的另一项关键贡献是构建了基于Benjamini-Yekutieli错误发现率校正的协变量层面p值变量选择程序。我们证明，当样本量n趋于无穷时，所得指标集以概率趋近于1与真实相关协变量集合完全一致。大量仿真实验表明，所提方法优于现有竞争方法，而对标普500收益率的实证研究则进一步验证了该变量选择框架的实际应用价值。