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

Kojadinovic, Ivan; Quessy, Jean‐François; Rohmer, Tom

doi:10.1007/s10463-015-0520-2

Cited by 14 publications

(13 citation statements)

References 27 publications

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“…The results are summarized in Table 4. We find the general picture mediated by Table 3 Kojadinovic et al (2016) also propose a bootstrapping procedure to obtain critical values for the improved Spearman (2014)). To illustrate this point, consider the following example: Suppose in the first half of the sequence that the observations are i.i.d., following the distribution of…”

Section: Simulation Resultsmentioning

confidence: 64%

“…We call the new proposal Kendall test. Moreover, we consider the improved Spearman test by Kojadinovic et al (2016). Throughout, we estimate the long-run variance σ 2 τ of the Kendall test by the estimatorσ 2 τ,n given by (7), where we choose the bandwidth b n = 2n 1/3 and κ to be the quartic kernel…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The reason lies in the usage of R n (•) instead of R k (•) in ( 12). Recently, Kojadinovic, Quessy, and Rohmer (2016) proposed a new constancy test for Spearman's rho which fixes this drawback and has therefore considerably higher power. Spearman's rho is asymptotically equivalent to a U -statistic of order 3, and an asymptotic analysis of the related test statistic…”

Section: Previous Proposalsmentioning

confidence: 99%

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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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Section: Simulation Resultsmentioning

confidence: 64%

Section: Simulation Resultsmentioning

confidence: 99%

Section: Previous Proposalsmentioning

confidence: 99%

See 1 more Smart Citation

Testing for Changes in Kendall’s Tau

Dehling¹,

Vogel

Wendler

et al. 2016

Econom. Theory

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“…Politis and White (2004) (see also Patton et al (2009)) derive optimal blocklengths for block bootstrap methods and obtain also an expression similar to (11). This technique is adapted, e.g., by Kojadinovic et al (2015) for a change-point test based on Spearman's rho. Furthermore, identified the asymptotically optimal blocklength for the multiplier bootstrap of U-statistics and developed a method to estimate it.…”

Section: Data-adaptive Bandwidth Selectionmentioning

confidence: 99%

Tests for Scale Changes Based on Pairwise Differences

Gerstenberger

Vogel

Wendler

2019

Journal of the American Statistical Association

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In many applications it is important to know whether the amount of fluctuation in a series of observations changes over time. In this article, we investigate different tests for detecting change in the scale of mean-stationary time series. The classical approach based on the CUSUM test applied to the squared centered, is very vulnerable to outliers and impractical for heavy-tailed data, which leads us to contemplate test statistics based on alternative, less outlier-sensitive scale estimators.It turns out that the tests based on Gini's mean difference (the average of all pairwise distances) or generalized Qn estimators (sample quantiles of all pairwise distances) are very suitable candidates. They improve upon the classical test not only under heavy tails or in the presence of outliers, but also under normality. An explanation for this counterintuitive result is that the corresponding long-run variance estimates are less affected by a scale change than in the case of the sample-variance-based test.We use recent results on the process convergence of U-statistics and U-quantiles for dependent sequences to derive the limiting distribution of the test statistics and propose estimators for the long-run variance. We perform a simulations study to investigate the finite sample behavior of the test and their power. Furthermore, we demonstrate the applicability of the new change-point detection methods at two real-life data examples from hydrology and finance.

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“…The finite-sample performance of the tests based on S n,A and S θ n,A was compared with that of two other tests for H 0 designed to be particularly sensitive to H 0,c in (1.3): the test based on the empirical copula studied in (statisticŠ n ) and the test based on Spearman's rho considered in Kojadinovic et al (2015) (statisticS n,1 ). Both tests rely on multiplier bootstraps for the computation of approximate p-values.…”

Section: Simulation Studymentioning

confidence: 99%

Detecting breaks in the dependence of multivariate extreme-value distributions

2016

Self Cite

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In environmental sciences, it is often of interest to assess whether the dependence between extreme measurements has changed during the observation period. The aim of this work is to propose a statistical test that is particularly sensitive to such changes. The resulting procedure is also extended to allow the detection of changes in the extreme-value dependence under the presence of known breaks in the marginal distributions. Simulations are carried out to study the finite-sample behavior of both versions of the proposed test. Illustrations on hydrological data sets conclude the work.

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

Cited by 14 publications

References 27 publications

Testing for Changes in Kendall’s Tau

Testing for Changes in Kendall’s Tau

Tests for Scale Changes Based on Pairwise Differences

Detecting breaks in the dependence of multivariate extreme-value distributions

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