Robust Nonparametric Testing for Structural Changes in Multivariate Volatility via Multiple Quantiles

2026-08-25

AI Summary

本文提出一种非参数检验方法，通过聚合多个分位数的广义分位数得分来检测多变量波动率矩阵中的结构变化，适用于重尾分布且无需指定备择假设下的波动动态。

Abstract

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.

Problem

• nonparametric test
• structural changes
• multivariate volatility
• quantiles
• U-statistic

Innovation

• nonparametric test
• structural changes
• multivariate volatility
• quantile scores
• U-statistic