A general procedure for change-point detection in multivariate time series

TL;DR

This paper introduces a versatile Wald-type statistic for detecting change-points in multivariate time series, applicable to various data types and based on a general contrast function, with proven consistency and demonstrated through simulations.

Contribution

It presents a unified, general procedure for change-point detection in multivariate time series using a flexible contrast-based Wald statistic, ensuring broad applicability and theoretical guarantees.

Findings

The proposed statistic converges to a known distribution under no change.

It diverges under the presence of a change, ensuring detection.

Simulation results confirm the theoretical asymptotic properties.

Abstract

We consider the change-point detection in multivariate continuous and integer valued time series. We propose a Wald-type statistic based on the estimator performed by a general contrast function; which can be constructed from the likelihood, a quasi-likelihood, a least squares method, etc. Sufficient conditions are provided to ensure that the statistic convergences to a well-known distribution under the null hypothesis (of no change) and diverges to infinity under the alternative; which establishes the consistency of the procedure. Some examples are detailed to illustrate the scope of application of the proposed procedure. Simulation experiments are conducted to illustrate the asymptotic results.