Changepoint detection for dependent Gaussian sequences

TL;DR

This paper introduces a practical method for detecting changepoints in autocorrelated Gaussian sequences using a CUSUM-type test, with thresholds derived from large deviations theory to control false alarms.

Contribution

It develops explicit threshold equations for dependent Gaussian data, improving false alarm control and variability management in changepoint detection.

Findings

Method performs well in simulations

Threshold equations effectively control false alarms

Applicable to ARMA processes

Abstract

In this paper easily applicable techniques are devised for detecting changepoints in autocorrelated Gaussian sequences. Our method proceeds by sequential evaluation of a CUSUM-type test statistic, which is compared to a predefined threshold. We assume that data is tested in sliding windows of fixed size. The distinguishing feature of this work is that, based on large deviations theory, we derive rather explicit equations that determine the threshold in such a way that the false alarm probability per window is approximately kept at the desired level. This criterion -- as opposed to the usual average run length -- allows to restrict not only the average number of false alarms but also their variability. Illustrative examples are provided, including the detection of a shift in mean in ARMA processes. The procedures are validated by means of a broad set of simulation experiments, and overall perform well.