A tail adaptive approach for change point detection
type: Item
instance of: scholarly article
title: A tail adaptive approach for change point detection
zbMATH Open document ID: 1411.62150
author: Bin Liu
author: Cheng Zhou
author: Xinsheng Zhang
published in: Journal of Multivariate Analysis
publication date: 2019-01-04T00:00:00Z
review text: Consider the problem of change point detection in multivariate data with unknown tails. Letting \(\mathbf{X}_1,\ldots,\mathbf{X}_n\) be \(d\)-dimensional data, which may be weakly dependent, with \(\mathbf{X}_i=(X_{i,1},\ldots,X_{i,d})\), the authors propose a tail-adaptive strategy to detect a single change point in \(E(\mathbf{X}_i)\) based on statistics of the form \[ \frac{1}{n^{3/2}}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{j=\lfloor nt\rfloor +1}^n\text{sgn}(X_{j,k}-X_{i,k})|X_{j,k}-X_{i,k}|^r\,, \] where the choice of \(r\) is governed by the tails of the data. The proposed test avoids the explicit estimation of the long-run covariance matrix using a bootstrap procedure. The limiting distribution of the test statistic under the null hypothesis that \(E(\mathbf{X}_1)=\cdots=E(\mathbf{X}_n)\) is calculated in terms of a \(d\)-dimensional Brownian bridge, under certain assumptions on the structure of the data. A tail-adaptive approach, considering a range of values of \(r\) simultaneously, is justified, which overcomes the need to know the tails of the data. The paper concludes with some numerical work, including a simulation study and an application to S\&P 500 data.
reviewed by: Fraser Daly
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62F40
Mathematics Subject Classification ID: 62P05
zbMATH DE Number: 6997743
zbMATH Keywords: change point test
zbMATH Keywords: low-cost bootstrap
zbMATH Keywords: tail adaptive test
zbMATH Keywords: two-sample \(U\)-statistics
MaRDI profile type: Publication
full work available at URL: j.jmva.2018.08.010
OpenAlex ID: W2889104583
cites work: Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation
cites work: Structural Breaks in Financial Time Series
cites work: Structural breaks in time series
cites work: Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. (With discussion)
cites work: Some asymptotic theory for the bootstrap
cites work: Numerical Tabulation of the Distribution of Kolmogorov's Statistic for Finite Sample Size
cites work: Limit theorems for functionals of mixing processes with applications to \(U\)-statistics and dimension estimation
cites work: Q5293978
cites work: The use of subseries values for estimating the variance of a general statistic from a stationary sequence
cites work: Q4101268
cites work: Q4348180
cites work: Invariance principles for changepoint problems
cites work: Change-Point Detection Under Dependence Based on Two-Sample U-Statistics
cites work: Power of change-point tests for long-range dependent data
cites work: Central limit theorem and the bootstrap for \(U\)-statistics of strongly mixing data
cites work: Law of the Iterated Logarithm for U-Statistics of Weakly Dependent Observations
cites work: Extreme Value Theory as a Risk Management Tool
cites work: A Class of Statistics with Asymptotically Normal Distribution
cites work: Testing for changes in multivariate dependent observations with an application to temperature changes
cites work: K-Sample Analogues of the Kolmogorov-Smirnov and Cramer-V. Mises Tests
cites work: Homogeneity and change-point detection tests for multivariate data using rank statistics
cites work: A test for a change in a parameter occurring at an unknown point
cites work: A Non-Parametric Approach to the Change-Point Problem
cites work: Q4869559
cites work: Changepoints in the North Atlantic Tropical Cyclone Record
cites work: Testing for Change Points in Time Series
cites work: Bootstrap for the sample mean and forU-statistics of mixing and near-epoch dependent processes
cites work: Q3948492
DOI: 10.1016/J.JMVA.2018.08.010
description: scientific article; zbMATH DE number 6997743