Detecting Tail Risk Differences in Multivariate Time Series
该研究推导了多变量时间序列中尾部指数估计的函数中心极限定理，并构建了检验多变量数据中尾部风险是否相等的统计方法，通过自归一化避免估计长期方差，模拟和汇率收益数据验证了方法的有效性。
We derive functional central limit theory for tail index estimates in multivariate time series under mild conditions on the extremal dependence between the components. We use this result to also derive convergence results for extreme value‐at‐risk and extreme expected shortfall estimates. This allows us to construct tests for equality of ‘tail risk’ in multivariate data, which can be useful in a number of empirical contexts. In constructing test statistics, we avoid estimating long‐run variances by using self‐normalization. Size and power of the tests for equal ‘tail risk’ are assessed in simulations. An empirical application to exchange returns illustrates the practical usefulness of the tests.