Autocorrelation Test under Frequent Mean Shifts

TL;DR

This paper introduces a Shift-Immune Portmanteau test for autocorrelation in time series data that remains reliable even when the mean undergoes frequent shifts, addressing a key limitation of classical methods.

Contribution

The paper proposes a novel autocorrelation testing framework that is robust to frequent mean shifts, improving analysis in complex non-stationary time series.

Findings

The SIP test effectively detects autocorrelation despite frequent mean shifts.

Application to nanopore sequencing data demonstrates practical utility.

The method outperforms traditional tests under non-stationary conditions.

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.