Change point estimation based on Wilcoxon tests in the presence of long-range dependence

TL;DR

This paper introduces a Wilcoxon-based estimator for detecting change points in the mean of long-range dependent sequences, demonstrating its consistency, convergence rate, and distributional properties, with applications to real data and simulations.

Contribution

It develops a new change point estimator using Wilcoxon tests tailored for long-range dependent data, establishing its theoretical properties and practical performance.

Findings

Achieves $1/n$ convergence rate for constant shift height.

Converges to a fractional Brownian motion functional when shift height decreases.

Performs well on real data and in simulations.

Abstract

We consider an estimator for the location of a shift in the mean of long-range dependent sequences. The estimation is based on the two-sample Wilcoxon statistic. Consistency and the rate of convergence for the estimated change point are established. In the case of a constant shift height, the $1/n$ convergence rate (with $n$ denoting the number of observations), which is typical under the assumption of independent observations, is also achieved for long memory sequences. It is proved that if the change point height decreases to $0$ with a certain rate, the suitably standardized estimator converges in distribution to a functional of a fractional Brownian motion. The estimator is tested on two well-known data sets. Finite sample behaviors are investigated in a Monte Carlo simulation study.