The sample ACF is the most common basic tool in analyzing time-series data. This paper provides a theoretical proof that, under some regularity conditions, sample ACF of a given stationary time series is not absolutely summable. Furthermore, it shows that under some mild conditions, the number of positive and negative sample ACFs and their absolute summation tend to infinity as the length of time series increases. The theoretical results are supported by practical evidence from a simulation study.

中文翻译：

---

关于样本自相关函数的绝对可和性

示例 ACF 是分析时间序列数据最常用的基本工具。本文提供了一个理论证明，即在某些规律性条件下，给定平稳时间序列的样本 ACF 不是绝对可和的。此外，它表明在一些温和条件下，随着时间序列长度的增加，正负样本 ACF 的数量及其绝对总和趋于无穷大。理论结果得到了模拟研究的实际证据的支持。