AI 中文总结
本文提出一种基于多分位数的多元波动率结构变化稳健非参数检验，规避高阶矩条件，聚合多分位数信息，经蒙特卡洛及Fama-French三因子模型验证有效。
AI 中文摘要
本文提出一种针对多元波动率矩阵结构变化的综合非参数检验方法。该检验在一系列分位数水平上聚合有界广义分位数得分，具有加权留q-交叉U统计量表示；删除邻近索引对可使序列依赖诱导的中心化效应渐近可忽略。所有实现所需的量（包括标准化所用的方差估计量）均在原假设下构造，无需指定备择假设下的波动率动态。标准化统计量收敛于标准正态分布。本文证明该检验对产生正积分分位数得分信号的固定备择假设具有一致性，并推导其对平滑偏离及趋近多重结构突变的愈发尖锐过渡具有非平凡的局部功效。有界得分构造规避了最小二乘和拟似然方法通常施加的有限四阶或八阶矩条件，而跨分位数聚合比单分位数方法利用了更多分布信息。蒙特卡洛结果显示，该方法在厚尾创新下具有满意的水平和良好的功效，在高斯创新下也有竞争力的表现。将其应用于Fama--French三因子模型，提供了全样本及多个经济相关子样本中因子协方差矩阵不平稳的证据。
英文摘要
We propose an omnibus nonparametric test for structural changes in the multivariate volatility matrix. The test aggregates bounded generalized quantile scores over a range of quantile levels and has a weighted leave-$q$-out $U$-statistic representation. Deleting nearby index pairs renders the centering effect induced by serial dependence asymptotically negligible. All quantities required for implementation, including the variance estimator used for standardization, are constructed under the null, without specifying volatility dynamics under the alternative. The standardized statistic converges to a standard normal distribution. We establish consistency against fixed alternatives that generate a positive integrated quantile-score signal and derive nontrivial local power against smooth departures and increasingly sharp transitions approaching multiple structural breaks. The bounded-score construction avoids the finite fourth- or eighth-moment conditions commonly imposed by least-squares and quasi-likelihood procedures, while aggregation across quantiles uses more distributional information than single-quantile methods. Monte Carlo results show satisfactory size and favorable power under heavy-tailed innovations, with competitive performance under Gaussian innovations. An application to the Fama--French three-factor model provides evidence against stability of the factor covariance matrix over the full sample and several economically relevant subsamples.
