Segmenting Time Series via Self-Normalisation

Zhao, Zifeng; Jiang, Feiyu; Shao, Xiaofeng

doi:10.1111/rssb.12552

Cited by 6 publications

(4 citation statements)

References 55 publications

(122 reference statements)

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“…Appendix C discusses in detail the choice of the tuning parameters for WCM.gSa. We investigate the performance of WCM.gSa on simulated datasets, in comparison with DeCAFS (Romano et al, 2022), DepSMUCE (Dette et al, 2020) and SNCP (Zhao et al, 2022) (the latter two applied with significance level

α = 0.05

). Here, we present the results from three representative settings and defer the descriptions of the full simulation results (from 13 scenarios with varying

n

, change point and serial dependence structures) and the competing methodologies to Appendix D, where we include DepSMUCE and SNCP applied with different choices of

α

as well as MACE proposed in Wu and Zhou (2020).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Under Assumption 2.2, we assume that there are finitely many change points with the spacing between the change points increasing linearly in n. A similar condition can be found in the literature addressing the problems of change point detection in the presence of serial correlations, see e.g. in Zhao et al (2022). The upper bound on |f ′ j | is a technical assumption made to distinguish the problem of detecting change points from that of outlier detection, see Cho and Kirch (2021) for further discussions.…”

Section: Theoretical Propertiesmentioning

confidence: 98%

“…Self-normalisation of test statistics avoids direct estimation of this nuisance parameter (Shao and Zhang, 2010;Pešta and Wendler, 2020) but theoretical investigation into its validity is often limited to change point testing, i.e. when there is at most a single change point, with the exception of Wu and Zhou (2020) and Zhao et al (2022), both of which adopt local window-based procedures. Consistency of the methods utilising penalised least squares estimation (Lavielle and Moulines, 2000) or Schwarz criterion (Cho and Kirch, 2022) constructed without further parametric assumptions, has been established under general conditions permitting serial dependence and heavy-tails.…”

Section: Introductionmentioning

confidence: 99%

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Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm

Cho,

Fryzlewicz

2023

Journal Time Series Analysis

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We propose a methodology for detecting multiple change points in the mean of an otherwise stationary, autocorrelated, linear time series. It combines solution path generation based on the wild contrast maximisation principle, and an information criterion‐based model selection strategy termed gappy Schwarz algorithm. The former is well‐suited to separating shifts in the mean from fluctuations due to serial correlations, while the latter simultaneously estimates the dependence structure and the number of change points without performing the difficult task of estimating the level of the noise as quantified e.g. by the long‐run variance. We provide modular investigation into their theoretical properties and show that the combined methodology, named WCM.gSa, achieves consistency in estimating both the total number and the locations of the change points. The good performance of WCM.gSa is demonstrated via extensive simulation studies, and we further illustrate its usefulness by applying the methodology to London air quality data.

show abstract

α = 0.05

). Here, we present the results from three representative settings and defer the descriptions of the full simulation results (from 13 scenarios with varying

n

, change point and serial dependence structures) and the competing methodologies to Appendix D, where we include DepSMUCE and SNCP applied with different choices of

α

as well as MACE proposed in Wu and Zhou (2020).…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Theoretical Propertiesmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm

Cho,

Fryzlewicz

2023

Journal Time Series Analysis

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“…A natural next step is to combine our test statistic that targets single change point with a generic segmentation algorithm, such as Wild Binary Segmentation [12], or Seeded Binary Segmentation [19]. Alternatively, it might be possible to extend the nested window based SN-segmentation approach in [42]. Further research along these directions are well underway.…”

Section: Discussionmentioning

confidence: 99%

Dimension-agnostic Change Point Detection

Gao¹,

Wang²,

Shao³

2023

Preprint

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Change point testing is a well-studied problem in statistics and there is a rich literature. Owing to the emergence of high-dimensional data with structural breaks, there has been a recent surge of interests in developing methods to accommodate the high-dimensionality. In practice, when the dimension is less than the sample size but is not small, it is often unclear whether a method that is tailored to highdimensional data or simply a classical method that is developed and justified for low-dimensional data, is preferred. In addition, the methods designed for low-dimensional data may not work well in the highdimensional environment and vice versa. This naturally brings up the question whether there is a change point test that can work for data of low, medium and high dimensions.In this paper, we first propose a dimension-agnostic testing procedure targeting at a single change point in the mean of multivariate time series. Our new test is inspired by recent work of [18], who formally developed the notion of "dimension-agnostic" in several testing problems for iid data. We develop a new test statistic by adopting their sample splitting and projection ideas, and combining it with the self-normalization method for time series [29,31]. Using a novel conditioning argument, we are able to show that the limiting null distribution for our test statistic is the same regardless of the dimensionality (fixed versus growing), and the magnitude of cross-sectional dependence (weak versus strong). The power analysis is also conducted to understand the large sample behavior of the proposed test. Furthermore, we present an extension to test for multiple change points in mean and derive the limiting distributions of the new test statistic under both the null and alternatives. Through Monte Carlo simulations, we show that the finite sample results strongly corroborate the theory and suggest that the proposed tests can be used as a benchmark for many time series data due to its robustness to weak temporal dependence, arbitrary cross-sectional dependence and a wide range of dimensionality.

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High-dimensional data segmentation in regression settings permitting temporal dependence and non-Gaussianity

Cho,

Owens

2024

Electron. J. Statist.

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Segmenting Time Series via Self-Normalisation

Cited by 6 publications

References 55 publications

Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm

Multiple change point detection under serial dependence: Wild contrast maximisation and gappy Schwarz algorithm

Dimension-agnostic Change Point Detection

High-dimensional data segmentation in regression settings permitting temporal dependence and non-Gaussianity

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