Power of change-point tests for long-range dependent data

Dehling, Herold; Rooch, Aeneas; Taqqu, Murad S.

doi:10.1214/17-ejs1283

Cited by 20 publications

(38 citation statements)

References 14 publications

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“…Here, we choose the Wilcoxon change-point test from [10] (see section 1) which rejects the null hypothesis H 0 (that there is no change in the mean) for large values of the test statistic…”

Section: Pre-estimating the Jumpmentioning

confidence: 99%

“…For more details see [10]. The change-point is supposed to take place after the observation X k * where k * ∈ {1, .…”

Section: Pre-estimating the Jumpmentioning

confidence: 99%

“…by [20], [28] or [50]. In [51] a test procedure based on Wilcoxon rank statistics is analysed, while [10] proposed a test which is based on the Wilcoxon two-sample test statistic:…”

mentioning

confidence: 99%

“…Upper quantiles of this asymptotic distribution can be used as critical values for the test. For details and critical values, see [10].…”

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confidence: 99%

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Estimation methods for the LRD parameter under a change in the mean

2016

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When analyzing time series which are supposed to exhibit long-range dependence (LRD), a basic issue is the estimation of the LRD parameter, for example the Hurst parameter H ∈ (1/2, 1). Conventional estimators of H easily lead to spurious detection of long memory if the time series includes a shift in the mean. This defect has fatal consequences in change-point problems: Tests for a level shift rely on H, which needs to be estimated before, but this estimation is distorted by the level shift.We investigate two blocks approaches to adapt estimators of H to the case that the time series includes a jump and compare them with other natural techniques as well as with estimators based on the trimming idea via simulations. These techniques improve the estimation of H if there is indeed a change in the mean.In the absence of such a change, the methods little affect the usual estimation. As adaption, we recommend an overlapping blocks approach: If one uses a consistent estimator, the adaption will preserve this property and it performs well in simulations.

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“…Here, we choose the Wilcoxon change-point test from [10] (see section 1) which rejects the null hypothesis H 0 (that there is no change in the mean) for large values of the test statistic…”

Section: Pre-estimating the Jumpmentioning

confidence: 99%

“…For more details see [10]. The change-point is supposed to take place after the observation X k * where k * ∈ {1, .…”

Section: Pre-estimating the Jumpmentioning

confidence: 99%

See 2 more Smart Citations

Estimation methods for the LRD parameter under a change in the mean

2016

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“…In fact, although stationary long-memory models are often employed in practice, there do not exist many tests for the hypothesis of stationarity which include these processes. Berkes et al (2006), Sibbertsen andKruse (2009) andDehling, Rooch, andTaqqu (2013) consider CUSUM and Wilcoxon type tests to discriminate between long-range dependence and one change in mean. A change with respect to the mean is of course only the simplest possible deviation from stationarity and there is particular interest in measuring deviations in the dependency structure over time as well.…”

Section: Introductionmentioning

confidence: 99%

Measuring stationarity in long-memory processes

Sen¹,

Preuß²,

Dette³

2017

STAT SINICA

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In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an L2-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap procedure to improve the approximation of the nominal level and prove its consistency. Throughout the paper, we work with Riemann sums of a squared periodogram instead of integrals (as it is usually done in the literature) and as a by-product of independent interest it is demonstrated that the two approaches behave differently in the limit.

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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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Power of change-point tests for long-range dependent data

Cited by 20 publications

References 14 publications

Estimation methods for the LRD parameter under a change in the mean

Estimation methods for the LRD parameter under a change in the mean

Measuring stationarity in long-memory processes

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

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