Uniform change point tests in high dimension

By Moritz Jirak. 2015

143 citations recorded by the source corpus.

Consider $d$ dependent change point tests, each based on a CUSUM-statistic. We provide an asymptotic theory that allows us to deal with the maximum over all test statistics as both the sample size $n$ and $d$ tend to infinity. We achieve this either by a consistent bootstrap or an appropriate limit distribution. This allows for the construction of simultaneous confidence bands for dependent change point tests, and explicitly allows us to determine the location of the change both in time and coordinates in high-dimensional time series. If the underlying data has sample size greater or equal $n$ for each test, our conditions explicitly allow for the large $d$ small $n$ situation, that is, where $n/d\to0$. The setup for the high-dimensional time series is based on a general weak dependence concept. The conditions are very flexible and include many popular multivariate linear and nonlinear models from the literature, such as ARMA, GARCH and related models. The construction of the tests is completely nonparametric, difficulties associated with parametric model selection, model fitting and parameter estimation are avoided. Among other things, the limit distribution for $\max_{1\leq h\leq d}\sup_{0\leq t\leq1}\vert \mathcal{W}_{t,h}-t\mathcal{W}_{1,h}\vert$ is established, where $\{\mathcal{W}_{t,h}\}_{1\leq h\leq d}$ denotes a sequence of dependent Brownian motions. As an application, we analyze all S&P 500 companies over a period of one year.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d144062364b8ca0bde05ae2ae481ae1ce865f3ab

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Citations in the corpus

Univariate mean change point detection: Penalization, CUSUM and optimality (2018, methodology): “Change point detection problems in high-dimensional means (e.g. Cho and Fryzlewicz, 2015; Cho, 2015; Aston and Kirch, 2014; Jirak, 2015; Wang and Samworth, 2018), in covariance structures (e.g. Aue et al., 2009; Avanesov and Buzun, 2016; Wang et al., 2017), in dynamic networks (e.g. Gibberd and…”
Change-point detection in high-dimensional covariance structure (2016, methodology): “As an alternative, permutation [28] [31] or parametric bootstrap may be used [28].”
Simultaneous multiple change-point and factor analysis for high-dimensional time series (2016, unknown): “For this, a number of methodologies have been investigated in the literature, such as Horváth and Hušková (2012), Enikeeva and Harchaoui (2015), Jirak (2015), Cho and Fryzlewicz (2015) and Wang and Samworth (2018).”
Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data (2017, methodology): “Nonparametric methods have been proposed for the change-point detection problem for multivariate/non-Euclidean observations as well (Jirak et al. (2015), Matteson and James (2014), Lung-Yut-Fong, L´evy-Leduc and Capp´e (2011), Cule, Samworth and Stewart (2010), Desobry, Davy and Don-carli (2005)).”
Change-point detection in panel data via double CUSUM statistic (2016, methodology): “Motivated by Jirak (2015), εt is generated from the following two models: (N1) ARMA(2, 2) model.”
Selective review of offline change point detection methods (2020, background): “In [150], the authors give a general discussion on how to aggregate 960 (dependant) change detection statistics, each based on a subset of an increasing 961 number of components.”