Inference for single and multiple change-points in time series

Jandhyala, Venkata K.; Fotopoulos, S.; MacNeill, Ian B.; Liu, Pengyu

doi:10.1111/jtsa12035

Cited by 58 publications

(73 citation statements)

References 137 publications

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“…Considering (22), (25) and the square of (24) together with the relationship V ar(Ȟw ,1 ) = O(π 2 /(24b) + o(1/b)) (see e.g. [22]) we observe that the following term is dominating:…”

Section: Proof Of Remark 2 (I)mentioning

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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“…Considering (22), (25) and the square of (24) together with the relationship V ar(Ȟw ,1 ) = O(π 2 /(24b) + o(1/b)) (see e.g. [22]) we observe that the following term is dominating:…”

Section: Proof Of Remark 2 (I)mentioning

confidence: 99%

“…All these methods have in common that they require knowledge of the LRD parameter of the data, be it D as in (3), the Hurst exponent H = 1 − D/2 or other related quantities to describe the intensity of LRD. For an overview about change-point analysis, see the book of [8] or the recent article by [25].…”

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confidence: 99%

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

2016

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“…On the other hand, estimation of an index is obviously a simpler problem than estimation of an entire measure. While the problem of detecting abrupt changes has been discussed intensively in a time series context [see Aue and Horváth (2013) and Jandhyala et al (2013) for a review of the literature], detecting gradual changes is a much harder problem and the methodology is not so well developed. Most authors consider nonparametric location or parametric models with independently distributed observations and we refer to Bissell (1984), Gan (1991), Siegmund and Zhang (1994), Husková (1999), Husková and Steinebach (2002) and Mallik et al (2013) among others [see also Aue and Steinebach (2002) for some results in a time series model].…”

Section: Introductionmentioning

confidence: 99%

Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes

Hoffmann

Vetter

Dette

2018

Stochastic Processes and their Applications

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In applications changes of the properties of a stochastic feature occur often gradually rather than abruptly, that is: after a constant phase for some time they slowly start to change. Efficient analysis for change points should address the specific features of such a smooth change. In this paper we discuss statistical inference for localizing and detecting gradual changes in the jump characteristic of a discretely observed Itō semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analyzed deriving new results on the weak convergence of a sequential empirical tail integral process and a corresponding multiplier bootstrap procedure.

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“…Since the seminal work on detecting structural breaks in the mean of Page (1954) a powerful methodology has been developed to detect various types of change points in time series [see for example Aue and Horváth (2013) and Jandhyala et al (2013) for recent reviews of the literature]. Several authors have argued that in applications besides the 1 Corresponding author.…”

Section: Introductionmentioning

confidence: 99%

Change Point Analysis of Correlation in Non-stationary Time Series

Dette¹,

Wu²,

Zhou³

2019

STAT SINICA

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A restrictive assumption in change point analysis is "stationarity under the null hypothesis of no change-point", which is crucial for asymptotic theory but not very realistic from a practical point of view. For example, if change point analysis for correlations is performed, it is not necessarily clear that the mean, marginal variance or higher order moments are constant, even if there is no change in the correlation. This paper develops change point analysis for the correlation structures under less restrictive assumptions. In contrast to previous work, our approach does not require that the mean, variance and fourth order joint cumulants are constant under the null hypothesis. Moreover, we also address the problem of detecting relevant change points.

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Inference for single and multiple change-points in time series

Cited by 58 publications

References 137 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

Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes

Change Point Analysis of Correlation in Non-stationary Time Series

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