Change-point analysis in frequency domain for chronological data

TL;DR

This paper introduces a new spectral density-based method for consistent change-point detection in time series, effective even with unknown means, variances, and outliers, validated through simulations and real data.

Contribution

It proposes a novel change-point estimation technique using only empirical spectral density and the Gauss-Newton algorithm, applicable with unknown moments.

Findings

Method accurately detects change-points in simulations.

Robust to outliers in real-world data.

Validates asymptotic properties of estimators.

Abstract

The purpose of this study is to provide a new methodology of how one can consistently estimate a change-point in time series data. In contrast with previous studies, the suggested methodology employs only the empirical spectral density and its first moment. This is accomplished when both the means and variances before and after the unidentified time point are unknown. Then, the well-known Gauss-Newton algorithm is applied to estimate and provide asymptotic results for the parameters involved. Simulations carried out under different distributions, sizes and unknown time points confirm the validity and accuracy of the methodology. The real-world example considered in the paper illustrates the robustness of the methodology in the presence of even extreme outliers.