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.

翻译：检验自相关是否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）依赖于平稳性假设，需要在应用前去除趋势或均值漂移等非平稳成分。然而，这在实际中并非总是可行，特别是当均值结构较为复杂时（例如具有频繁漂移的分段常数形式）。本文针对频繁均值漂移下的时间序列数据，提出了一种新的自相关推断框架。具体而言，我们引入了一种漂移免疫混合（SIP）检验，该检验能够可靠地检测自相关，并对均值漂移具有鲁棒性。我们通过纳米孔测序数据的应用实例展示了该方法的效果。