Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

Aue, Alexander; Rice, Gregory; Sönmez, Ozan

doi:10.1111/rssb.12257

Cited by 92 publications

(164 citation statements)

References 33 publications

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“…To test H 0,2 versus H A ,2 , we define analogously to F T and F T , p ,

Z_{T} = T \sup_{0 \leq x \leq 1} ‖ Ĉ_{X Y} (\cdot, \cdot, x) - x Ĉ_{X Y} (\cdot, \cdot, 1) ‖_{2}^{2} .

and

Z_{T, p} = T \sup_{0 \leq x \leq 1} {falsefalse}_{\sum}^{i = 1} \frac{⟨ Ĉ_{X Y} (\cdot, \cdot, x) - x Ĉ_{X Y} (\cdot, \cdot, 1), {\hat{φ}}_{i}_{2}^{2}}{{\hat{λ}}_{i}} .

Z T and Z T , p are each maximally selected CUSUM type statistics based on comparing the partial sample estimates of C XY to the estimator from the whole sample. These statistics are similar to those considered in Aue et al (), Aston and Kirch (), and Sharipov et al (). The following corollaries of Theorem quantify the large sample behavior of these statistics under H 0,2 .…”

Section: Inference For the Cross‐covariance Functionsupporting

confidence: 90%

“…In the case of the norm based test, errors in estimating small eigenvalues have a negligible effect, since they manifest as small changes in the estimated limiting distribution, while the projection based tests can be greatly affected by small estimation errors of the eigenvalues. A similar observation is made in the context of change point analysis in Aue et al ().…”

Section: Simulation Studysupporting

confidence: 78%

“…Z T and Z T,p are each maximally selected CUSUM type statistics based on comparing the partial sample estimates of C XY to the estimator from the whole sample. These statistics are similar to those considered in Aue et al (2018), Aston and Kirch (2012), and Sharipov et al (2016). The following corollaries of Theorem 2.1 quantify the large sample behavior of these statistics under H 0,2 .…”

Section: Inference For the Cross-covariance Functionmentioning

confidence: 52%

See 2 more Smart Citations

Inference for the Lagged Cross‐Covariance Operator Between Functional Time Series

Rice

Shum

2019

Journal Time Series Analysis

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When considering two or more time series of functional data objects, for instance those derived from densely observed intraday stock price data of several companies, the empirical cross‐covariance operator is of fundamental importance due to its role in functional lagged regression and exploratory data analysis. Despite its relevance, statistical procedures for measuring the significance of such estimators are currently undeveloped. We present methodology based on a functional central limit theorem for conducting statistical inference for the cross‐covariance operator estimated between two stationary, weakly dependent, functional time series. Specifically, we consider testing the null hypothesis that the two series possess a specified cross‐covariance structure at a given lag. Since this test assumes that the series are jointly stationary, we also develop a change‐point detection procedure to validate this assumption of independent interest. The most imposing technical hurdle in implementing the proposed tests involves estimating the spectrum of a high dimensional spectral density operator at frequency zero. We propose a simple dimension reduction procedure based on functional principal component analysis to achieve this, which is shown to perform well in a simulation study. We illustrate the proposed methodology with an application to densely observed intraday price data of stocks listed on the New York stock exchange‐20.40

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“…To test H 0,2 versus H A ,2 , we define analogously to F T and F T , p ,

Z_{T} = T \sup_{0 \leq x \leq 1} ‖ Ĉ_{X Y} (\cdot, \cdot, x) - x Ĉ_{X Y} (\cdot, \cdot, 1) ‖_{2}^{2} .

and

Z_{T, p} = T \sup_{0 \leq x \leq 1} {falsefalse}_{\sum}^{i = 1} \frac{⟨ Ĉ_{X Y} (\cdot, \cdot, x) - x Ĉ_{X Y} (\cdot, \cdot, 1), {\hat{φ}}_{i}_{2}^{2}}{{\hat{λ}}_{i}} .

Section: Inference For the Cross‐covariance Functionsupporting

confidence: 90%

Section: Simulation Studysupporting

confidence: 78%

Section: Inference For the Cross-covariance Functionmentioning

confidence: 52%

See 1 more Smart Citation

Inference for the Lagged Cross‐Covariance Operator Between Functional Time Series

Rice

Shum

2019

Journal Time Series Analysis

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is a common method to use the time point in which the maximum is attained as an estimator for the time of the change. This procedure was investigated by Aue et al () for independent functional observations and by Aue, Rice, & Sönmez () for functional time series.…”

Section: Real‐life Data Examplesmentioning

confidence: 99%

Sequential block bootstrap in a Hilbert space with application to change point analysis

2016

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A new test for structural changes in functional data is investigated. It is based on Hilbert space theory and critical values are deduced from bootstrap iterations. Thus a new functional central limit theorem for the block bootstrap in a Hilbert space is required. The test can also be used to detect changes in the marginal distribution of random vectors, which is supplemented by a simulation study. Our methods are applied to hydrological data from Germany. The Canadian Journal of Statistics 44: 300–322; 2016 © 2016 Statistical Society of Canada

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“…This can be done in several ways; see Lu, Lund, and Lee () for a different approach for detecting multiple breaks in climate time series. Two approaches were discussed in Sönmez (), namely, binary segmentation based on the method of Aue, Rice, and Sönmez () and moving average smoothing. Because both methods led to almost identical conclusion s in terms of the structural break analysis for the mean curve, thus indicating some robustness with respect to the method of detrending, only results for binary segmentation are reported here.…”

Section: Application To Annual Temperature Profilesmentioning

confidence: 99%

Structural break analysis for spectrum and trace of covariance operators

2019

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This paper deals with analyzing structural breaks in the covariance operator of sequentially observed functional data. For this purpose, procedures are developed to segment an observed stretch of curves into periods for which second-order stationarity may be reasonably assumed. The proposed methods are based on measuring the fluctuations of sample eigenvalues, either individually or jointly, and traces of the sample covariance operator computed from segments of the data. To implement the tests, new limit results are introduced that deal with the large-sample behavior of vector-valued processes built from partial sample eigenvalue estimates. These results in turn enable the calibration of the tests to a prescribed asymptotic level. Applications to Australian annual minimum temperature curves and sea surface temperature anomaly records confirm that the proposed methods work well in finite samples. The first application suggests that the variation in annual minimum temperature underwent a structural break in the 1950s, after which typical fluctuations from the generally increasing trend started to be significantly smaller. KEYWORDS annual temperature profiles, change-point analysis, functional data, functional principal components, functional time series, structural breaks MSC CLASSIFICATION 62G99, 62H99, Secondary: 62M10, 91B84 Environmetrics. 2020;31:e2617.wileyonlinelibrary.com/journal/env

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Detecting and Dating Structural Breaks in Functional Data Without Dimension Reduction

Cited by 92 publications

References 33 publications

Inference for the Lagged Cross‐Covariance Operator Between Functional Time Series

Inference for the Lagged Cross‐Covariance Operator Between Functional Time Series

Sequential block bootstrap in a Hilbert space with application to change point analysis

Structural break analysis for spectrum and trace of covariance operators

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