Multiscale change point detection for dependent data

Holger Dette · Mathias Vetter

41 citations0/0 files storedScandinavian Journal of Statistics

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Advanced Statistical Process Monitoring Statistical Methods and Inference Advanced Statistical Methods and Models

Abstract

Abstract In this article we study the theoretical properties of the simultaneous multiscale change point estimator (SMUCE) in piecewise‐constant signal models with dependent error processes. Empirical studies suggest that in this case the change point estimate is inconsistent, but it is not known if alternatives suggested in the literature for correlated data are consistent. We propose a modification of SMUCE scaling the basic statistic by the long run variance of the error process, which is estimated by a difference‐type variance estimator calculated from local means from different blocks. For this modification we prove model consistency for physical‐dependent error processes and illustrate the finite sample performance by means of a simulation study.

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References

2012Optimal Detection of Changepoints With a Linear Computational Cost 2014Wild binary segmentation for multiple change-point detection 1988Estimating the number of change-points via Schwarz' criterion 2013A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data 2014Multiscale Change Point Inference 2000Least‐squares Estimation of an Unknown Number of Shifts in a Time Series 2016A computationally efficient nonparametric approach for changepoint detection 2017A MOSUM procedure for the estimation of multiple random change points

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2021mosum: A Package for Moving Sums in Change-Point Analysis 2022Optimal difference-based variance estimators in time series: A general framework 2023Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm 2021Are deviations in a gradually varying mean relevant? A testing approach based on sup-norm estimators 2022Bootstrap confidence intervals for multiple change points based on moving sum procedures

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