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：股票市场指标等多时间序列的聚类所产生的传染效应会进一步复杂化波动性的本质，导致依赖渐近分布的参数检验在检验水平和功效方面存在问题。我们提出了一种基于多时间序列自助法的波动性检验方法，旨在考虑可能存在的传染效应。该检验对分布假设具有较好的稳健性，但其表现取决于波动性的具体特性。即使在时间序列接近非平稳的情况下，该检验仍能保持正确的检验水平。当时间序列在均值上平稳且波动性仅集中在较少聚类中时，该检验尤其有效。我们通过全球股价数据对该方法进行了实证演示。