Title: Autocorrelation Test under Frequent Mean Shifts Show Chinese title

Title: 频繁均值变化下的自相关性检验

Abstract: Testing for the presence of autocorrelation is a fundamental problem in time series analysis. Classical methods such as the Box-Pierce test rely on the assumption of stationarity, necessitating the removal of non-stationary components such as trends or shifts in the mean prior to application. However, this is not always practical, particularly when the mean structure is complex, such as being piecewise constant with frequent shifts. In this work, we propose a new inferential framework for autocorrelation in time series data under frequent mean shifts. In particular, we introduce a Shift-Immune Portmanteau (SIP) test that reliably tests for autocorrelation and is robust against mean shifts. We illustrate an application of our method to nanopore sequencing data. Show Chinese abstract

Abstract: 检测自相关性的存在是时间序列分析中的一个基本问题。 经典方法如Box-Pierce检验依赖于平稳性的假设，需要在应用之前去除非平稳成分，如趋势或均值的变化。 然而，这并不总是实际的，特别是在均值结构复杂的情况下，例如均值是分段常数且频繁变化的情况。 在本工作中，我们提出了一种在频繁均值变化下对时间序列数据中自相关性的新推断框架。 特别是，我们引入了一个抗位移的综合检验（SIP）检验，该检验能够可靠地检测自相关性，并且对均值变化具有鲁棒性。 我们展示了该方法在纳米孔测序数据中的应用。