A consistent clustering-based approach to estimating the number of change-points in highly dependent time-series

TL;DR

This paper introduces a clustering-based method for estimating the number of change-points in highly dependent time-series, providing a consistent approach under certain conditions and demonstrating its effectiveness through empirical evaluation.

Contribution

It proposes a novel clustering algorithm that estimates change-points in dependent time-series when the number of underlying distributions is known, addressing a key challenge in the field.

Findings

Algorithm is asymptotically consistent.

Method accurately estimates change-points in empirical tests.

Provides a practical solution under realistic assumptions.

Abstract

The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is provably impossible. However, it is shown that a consistent clustering method may be used to estimate the number of change points, under the additional constraint that the correct number of process distributions that generate the data is provided. This additional parameter has a natural interpretation in many real-world applications. An algorithm is proposed that estimates the number of change-points and locates the changes. The proposed algorithm is shown to be asymptotically consistent; its empirical evaluations are provided.