Multiscale change point detection for dependent data

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. K E Y W O R D S change point detection, multiscale methods, physical-dependent processes 1 INTRODUCTION The problem of detecting multiple abrupt changes in the structural properties of a time series and to split the data into several "stationary" segments has been of interest to statisticians for many decades. An efficient a posteriori change-point detection rule enables the researcher to analyze data under the assumption of piecewise-stationarity and has numerous applications including

Detecting multiple generalized change-points by isolating single ones

“…Recently, Dette et al. ( 2018 ) have attempted to treat this issue, specifically for the SMUCE approach of Frick et al. ( 2014 ), using a reliable estimate for the long run variance, , of the error distribution, which is not necessarily Gaussian.…”

A Variational View on Statistical Multiscale Estimation

“…Extensions can be found e.g. in Pein et al (2017) for heterogeneous Gaussian error, in Vanegas et al (2021) for general independent data, in Dette et al (2020) for dependent data, and in for automatic selecting the bins in a histogram and exploratory data analysis. Besides, Behr et al (2018) extended the MCPS to blind source separation, more precisely, to recover piecewise constant functions (taking values in a finite set) from noisy measurements of their mixtures.…”

mosum: A Package for Moving Sums in Change-Point Analysis

“…The distributional convergence and thus the thresholds associated with the corresponding critical values as discussed in Section 2.1, remain valid as long as the variance estimators σ 2 k are replaced by appropriate estimators for the long-run variance τ 2 = lim n→∞ var( √ nē n ) withē n = n −1 n t=1 e t . For this, we may use the MOSUM-version of the flat-top kernel estimator (Politis and Romano 1995) calculated with sufficiently large bandwidths (e.g., G ≥ 50), or the difference-based estimators from Tecuapetla-Gómez and Munk (2017), Dette, Eckle, and Vetter (2020) and Axt and Fried (2019). This is not recommended in the presence of frequent changes, however, as accurate estimation of the long-run variance is typically very difficult and thus estimators based on small and medium-sized samples are not very reliable.…”