Contagion arising from clustering of multiple time series like those in the stock market indicators can further complicate the nature of volatility, rendering a parametric test (relying on asymptotic distribution) to suffer from issues on size and power. We propose a test on volatility based on the bootstrap method for multiple time series, intended to account for possible presence of contagion effect. While the test is fairly robust to distributional assumptions, it depends on the nature of volatility. The test is correctly sized even in cases where the time series are almost nonstationary. The test is also powerful specially when the time series are stationary in mean and that volatility are contained only in fewer clusters. We illustrate the method in global stock prices data.

翻译：股票市场指标等多重时间序列的聚类现象所引发的传染效应会进一步加剧波动性的复杂特性，使得依赖渐近分布的参数检验在检验尺度和检验功效方面存在问题。本文提出一种基于自助法的多重时间序列波动性检验方法，旨在应对可能存在的传染效应。该检验方法对分布假设具有较强稳健性，但其有效性取决于波动性的本质特征。即使在时间序列接近非平稳的情况下，该检验仍能保持合理的检验尺度。特别是当时间序列均值平稳且波动仅集中在少数聚类中时，该检验具有显著功效。我们通过全球股票价格数据验证了该方法的有效性。