We consider cross‐sectional aggregation of time series with long‐range dependence. This question arises for instance from the statistical analysis of networks where aggregation is defined via routing matrices. Asymptotically, aggregation turns out to increase dependence substantially, transforming a hyperbolic decay of autocorrelations to a slowly varying rate. This effect has direct consequences for statistical inference. For instance, unusually slow rates of convergence for nonparametric trend estimators and nonstandard formulas for optimal bandwidths are obtained. The situation changes, when time‐dependent aggregation is applied. Suitably chosen time‐dependent aggregation schemes can preserve a hyperbolic rate or even eliminate autocorrelations completely.

中文翻译：

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关于高度依赖的时间序列的汇总

我们考虑具有长期依赖性的时间序列的横截面聚合。例如，该问题来自网络的统计分析，其中通过路由矩阵定义了聚合。渐近地，聚合结果证明实质上增加了依赖性，将自相关的双曲线衰减转换为缓慢变化的速率。这种影响直接影响到统计推断。例如，获得了非参数趋势估计器的异常慢的收敛速度和最优带宽的非标准公式。当应用基于时间的聚合时，情况发生了变化。适当选择的时间依赖性聚合方案可以保存双曲线速率或甚至完全消除自相关。