Change point detection and inference in multivariable nonparametric models under mixing conditions

TL;DR

This paper develops new methods for detecting and inferring change points in multivariate nonparametric time series with dependence, providing limiting distributions and consistent estimators for change point localization.

Contribution

It introduces the first limiting distribution results for change point estimators under vanishing or constant jump sizes in dependent multivariate data, along with new consistent estimators.

Findings

Derived limiting distributions for change point estimators.

Proposed a consistent change point detection method for dependent data.

Validated theoretical results with numerical experiments.

Abstract

This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be piecewise constant with densities in a H\"{o}lder class. The change points, or times at which the distribution changes, are unknown. We derive the limiting distributions of the change point estimators when the minimal jump size vanishes or remains constant, a first in the literature on change point settings. We are introducing two new features: a consistent estimator that can detect when a change is happening in data with short-term dependence, and a consistent block-type long-run variance estimator. Numerical evidence is provided to back up our theoretical results.