Change‐points and bootstrap

Gombay, Edit; Horváth, Lajos

doi:10.1002/(sici)1099-095x(199911/12)10:6<725::aid-env387>3.3.co;2-b

Cited by 16 publications

(30 citation statements)

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“…The following two results extend Theorems 2.1, 2.2 and 2.3 of Gombay and Horváth (1999) and suggest, for large n and under the null hypothesis, to interpret each of p D n and q D n as an "almost" independent copy of D n .…”

Section: Application To Change-point Detectionsupporting

confidence: 75%

“…With resampling in mind, we define two multiplier versions of D n based on the multiplier versions of Z n defined in the previous subsection. For any s P r0, 1s and f P F , let q D n ps, f q " t1´λ n psqu q Z n ps, f q´λ n psqt q Z n p1, f q´q Z n ps, f qu " q Z n ps, f q´λ n psq q Z n p1, f q, and, following Gombay and Horváth (1999), let p D n ps, f q " t1´λ n psqu p Z n ps, f q´λ n psq p Z ‹ n ps, f q,…”

Section: Application To Change-point Detectionmentioning

confidence: 99%

“…In this paper, we revisit and extend the approach proposed by Gombay and Horváth (1999) based on the test statistic…”

Section: Introductionmentioning

confidence: 99%

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Nonparametric tests for change-point detection à la Gombay and Horváth

Holmes

Kojadinovic

Quessy

2013

Journal of Multivariate Analysis

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International audienceThe nonparametric test for change-point detection proposed by Gombay and Horváth is revisited and extended in the broader setting of empirical process theory. The resulting testing procedure for potentially multivariate observations is based on a sequential generalization of the functional multiplier central limit theorem and on modifications of Gombay and Horváth's seminal approach that appears to improve the finite-sample behavior of the tests. A large number of candidate test statistics based on processes indexed by lower-left orthants and half-spaces are considered and their performance is studied through extensive Monte Carlo experiments involving univariate, bivariate and trivariate data sets. Finally, practical recommendations are provided and the tests are illustrated on trivariate hydrological data. © 2012 Elsevier Inc

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Section: Application To Change-point Detectionsupporting

confidence: 75%

Section: Application To Change-point Detectionmentioning

confidence: 99%

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Nonparametric tests for change-point detection à la Gombay and Horváth

Holmes

Kojadinovic

Quessy

2013

Journal of Multivariate Analysis

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“…Several nonparametric tests designed to be particularly sensitive to certain alternatives under H 0,m ∩ ¬H 0,c were proposed in the literature. Tests for the constancy of Kendall's tau (which is a functional of C) were investigated by Gombay and Horváth (1999) (see also Gombay and Horváth, 2002) and in the case of serially independent observations. A version of the previous tests adapted to a very general class of bivariate time series was proposed by Dehling et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Testing the constancy of Spearman’s rho in multivariate time series

2015

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A class of tests for change-point detection designed to be particularly sensitive to changes in the cross-sectional rank correlation of multivariate time series is proposed. The derived procedures are based on several multivariate extensions of Spearman's rho. Two approaches to carry out the tests are studied: the first one is based on resampling, the second one consists of estimating the asymptotic null distribution. The asymptotic validity of both techniques is proved under the null for strongly mixing observations. A procedure for estimating a key bandwidth parameter involved in both approaches is proposed, making the derived tests parameter-free. Their finite-sample behavior is investigated through Monte Carlo experiments. Practical recommendations are made and an illustration on trivariate financial data is finally presented.

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“…Several authors have used U -statistics for change-point problems before (e.g. Gombay and Horváth, 1995;Gombay and Horváth, 1999). The main contribution of the present paper is the thorough treatment of dependent series.…”

mentioning

confidence: 95%

Testing for Changes in Kendall’s Tau

Dehling¹,

Vogel

Wendler

et al. 2016

Econom. Theory

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For a bivariate time series ((X i , Y i )) i=1,...,n we want to detect whether the correlation between X i and Y i stays constant for all i = 1, . . . , n. We propose a nonparametric change-point test statistic based on Kendall's tau. The asymptotic distribution under the null hypothesis of no change follows from a new U -statistic invariance principle for dependent processes. Assuming a single change-point, we show that the location of the change-point is consistently estimated. Kendall's tau possesses a high efficiency at the normal distribution, as compared to the normal maximum likelihood estimator, Pearson's moment correlation. Contrary to Pearson's correlation coefficient, it shows no loss in efficiency at heavy-tailed distributions, and is therefore particularly suited for financial data, where heavy tails are common. We assume the data ((X i , Y i )) i=1,...,n to be stationary and P -near epoch dependent on an absolutely regular process. The P -near epoch dependence condition constitutes a generalization of the usually considered L p -near epoch dependence allowing for arbitrarily heavy-tailed data. We investigate the test numerically, compare it to previous proposals, and illustrate its application with two real-life data examples.Keywords: Change-point analysis, Kendall's tau, U -statistic, functional limit theorem, near epoch dependence in probability the association of financial price processes and, within reasonable time frames, re-estimate the correlation parameters. Particularly, in times of global financial crises, the price processes of most financial assets tend to be highly dependent, united in their common downward trend, causing the hedging powers of investment diversification to cease -an effect for which the term diversification meltdown has been coined. The problem of detecting changes in the distribution of sequential observations has a long history in statistics, see e.g. Csörgő and Horváth (1997). However, particularly detecting changes in the dependence structure of multivariate time series has attracted the focus of statistical research only recently. Examples for such detection procedures are Loretan and Phillips (1994), who test for covariance stationarity of a possibly heavy-tailed time series, Giacomini, Härdle, and Spokoiny (2009), who consider tests for homogeneity of time-varying copulae, Aue, Hörmann, Horváth, and Reimherr (2009), who propose a test for a constant covariance matrix, and Wied, Krämer, and Dehling (2012), who suggest a change-point test for correlations between two random variables based on Pearson's correlation coefficient. With this paper, we want to contribute to the literature by proposing a new test for constant Kendall's tau that can be applied to dependent series. We recommend to use the rank correlation measure Kendall's tau instead of Pearson's correlation coefficient because it is almost as efficient as the moment correlation at normality, but is significantly more efficient at heavytailed distributions. For details see Section 5. This issue is very im...

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Change‐points and bootstrap

Cited by 16 publications

References 0 publications

Nonparametric tests for change-point detection à la Gombay and Horváth

Nonparametric tests for change-point detection à la Gombay and Horváth

Testing the constancy of Spearman’s rho in multivariate time series

Testing for Changes in Kendall’s Tau

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