A breakpoint detection in the mean model with heterogeneous variance on fixed time-intervals

TL;DR

This paper introduces a new method for detecting change points in the mean of Gaussian processes with varying variance on fixed intervals, motivated by GNSS water vapor data analysis.

Contribution

It proposes a two-step segmentation model that estimates variances robustly before detecting mean change points, addressing limitations of existing dynamic programming methods.

Findings

The method performs well in simulation experiments.

Application to GNSS data successfully identifies abrupt changes.

The approach effectively handles heteroscedasticity in the data.

Abstract

This work is motivated by an application for the homogeneization of GNSS-derived IWV (Integrated Water Vapour) series. Indeed, these GPS series are affected by abrupt changes due to equipment changes or environemental effects. The detection and correction of the series from these changes is a crucial step before any use for climate studies. In addition to these abrupt changes, it has been observed in the series a non-stationary of the variability. We propose in this paper a new segmentation model that is a breakpoint detection in the mean model of a Gaussian process with heterogeneous variance on known time-intervals. In this segmentation case, the dynamic programming (DP) algorithm used classically to infer the breakpoints can not be applied anymore. We propose a procedure in two steps: we first estimate robustly the variances and then apply the classical inference by plugging these estimators. The performance of our proposed procedure is assessed through simulation experiments. An application to real GNSS data is presented.