Multiple‐change‐point detection for high dimensional time series via sparsified binary segmentation

By Haeran Cho, Piotr Fryzlewicz. 2015

404 citations recorded by the source corpus.

Time series segmentation, which is also known as multiple‐change‐point detection, is a well‐established problem. However, few solutions have been designed specifically for high dimensional situations. Our interest is in segmenting the second‐order structure of a high dimensional time series. In a generic step of a binary segmentation algorithm for multivariate time series, one natural solution is to combine cumulative sum statistics obtained from local periodograms and cross‐periodograms of the components of the input time series. However, the standard ‘maximum’ and ‘average’ methods for doing so often fail in high dimensions when, for example, the change points are sparse across the panel or the cumulative sum statistics are spuriously large. We propose the sparsified binary segmentation algorithm which aggregates the cumulative sum statistics by adding only those that pass a certain threshold. This ‘sparsifying’ step reduces the influence of irrelevant noisy contributions, which is particularly beneficial in high dimensions. To show the consistency of sparsified binary segmentation, we introduce the multivariate locally stationary wavelet model for time series, which is a separate contribution of this work.

Subfields: Applied Mathematics, Artificial Intelligence, Signal Processing

View Paper: https://www.semanticscholar.org/paper/64cdec145924a42e39dab03e461109603339d238

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Citations in the corpus

Uniform change point tests in high dimension (2015, methodology): “Using a threshold-aggregation approach, [15] study the detection of global changes (see also [27, 41]), whereas in [34], the topic of possible gain or loss in power in higher dimension is discussed.”
A Survey of Methods for Time Series Change Point Detection (2016, neutral): “The most familiar change point algorithm is cumulative sum [7,10,18,33], which accumulates deviations relative to a specified target of incomingmeasurements and indicates that a change point exists when the cumulative sum exceeds a specified threshold.”
Simultaneous multiple change-point and factor analysis for high-dimensional time series (2016, methodology): “…the factor structure, with accompanying change-point tests and estimators for its location, can be found in Breitung and Eickmeier (2011), Chen et al. (2014), Han and Inoue (2014), Corradi and Swanson (2014), Yamamoto and Tanaka (2015), Baltagi et al. (2017), Bai et al. (2017) and Massacci (2017).”
Finite sample change point inference and identification for high‐dimensional mean vectors (2017, background): “[19] consider the estimation problem of change points in the (marginal) variances of high-dimensional time series under a multiplicative model.”
Wild binary segmentation for multiple change-point detection (2014, methodology): “BS is used for univariate time series segmentation in Fryzlewicz and Subba Rao (2014) and Cho and Fryzlewicz (2012), and for multivariate, possibly high-dimensional time series segmentation in Cho and Fryzlewicz (2014).”
Change-point detection in high-dimensional covariance structure (2016, methodology): “We also thank Jun Li and Haeran Cho for providing the implementation of the approach proposed in [30] and in [12] respectively.”
Detection of change in the spatiotemporal mean function (2017, background): “Keywords: Change point; Functional data; Mean function; Spatiotemporal data”
Detecting relevant changes in time series models (2014, methodology): “One obvious idea is to use binary segmentation methods for this problem (see for example Cho and Fryzlewicz (2015)), but multiscale inference (see Frick et al. (2014)) or methods based on spectral analysis (see for example Preuss et al. (2014)) might yield to other powerful methods.”
Univariate mean change point detection: Penalization, CUSUM and optimality (2018, background): “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…”