This paper derives the limit distribution of the rescaled sum of the absolute value of an integrated process with continuously distributed innovations raised to a negative power less than $-$ 1, and of the analogous statistic that is obtained using the same function of an integrated process but only considering positive values of the integrated process. We show that the limit behavior of this statistic is determined by the values of the integrated process that are closest to 0, and find the limit behavior of the values of the integrated process that are closest to 0.

中文翻译：

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综合流程的负面影响

本文推导了重新调整后的集成过程绝对值总和的极限分布，其中连续分布的创新提高到小于 $-$ 1 的负幂，以及使用集成过程的相同函数获得的类似统计量的极限分布但只考虑集成过程的积极价值。我们证明了这个统计量的极限行为是由最接近 0 的集成过程的值决定的，并找到最接近 0 的集成过程的值的极限行为。