A bootstrap test for time series linearity

Berg, Arthur; Paparoditis, Efstathios; Politis, Dimitris N.

doi:10.1016/j.jspi.2010.04.047

Cited by 25 publications

(22 citation statements)

References 65 publications

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“…Conditions like (4.8)−(4.10) are standard in the context of parametric bootstraps [see for example Berg, Paparoditis, and Politis (2010) or Kreiß, Paparoditis, and Politis (2011)] and a detailed discussion of them is given in . There it is also discussed why (4.10) might hold in the general framework considered here, but a rigorous proof of such a statement is an open problem so far.…”

Section: The Estimate In (D) Also Holds If the Null Hypothesis (37) mentioning

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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Section: The Estimate In (D) Also Holds If the Null Hypothesis (37) mentioning

confidence: 99%

Measuring stationarity in long-memory processes

Sen¹,

Preuß²,

Dette³

2017

STAT SINICA

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“…More precisely we will now develop a bootstrap procedure, which is closely related to the one dimensional AR(∞) bootstrap introduced by Kreiss (1988). This methodology has found considerable attention in the recent literature [see Choi and Hall (2000), Goncalves and Kilian (2007) or Berg et al (2010) among others] since it is easy to implement but has sufficient complexity to capture the predominant dependencies in the underlying process. In the present context it will yield critical values such that a test for structural breaks based on the statisticD T is directly implementable.…”

Section: Testing For Structural Breaksmentioning

confidence: 99%

“…Note that all assumptions of Theorems 3.5 and 3.6 are rather standard in the framework of AR(∞) bootstrap [see for example Berg et al (2010) or Kreiss et al (2011) among others]…”

Section: Testing For Structural Breaksmentioning

confidence: 99%

Detection of Multiple Structural Breaks in Multivariate Time Series

Preuß

Puchstein

Dette

2015

Journal of the American Statistical Association

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We propose a new nonparametric procedure for the detection and estimation of multiple structural breaks in the autocovariance function of a multivariate (secondorder) piecewise stationary process, which also identifies the components of the series where the breaks occur. The new method is based on a comparison of the estimated spectral distribution on different segments of the observed time series and consists of three steps: it starts with a consistent test, which allows to prove the existence of structural breaks at a controlled type I error. Secondly, it estimates sets containing possible break points and finally these sets are reduced to identify the relevant structural breaks and corresponding components which are responsible for the changes in the autocovariance structure. In contrast to all other methods which have been proposed in the literature, our approach does not make any parametric assumptions, is not especially designed for detecting one single change point and addresses the problem of multiple structural breaks in the autocovariance function directly with no use of the binary segmentation algorithm. We prove that the new procedure detects all components and the corresponding locations where structural breaks occur with probability converging to one as the sample size increases and provide data-driven rules for

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“…In Section A.1.1, we establish (3.11), thus completing (but for Lemmas A.1-A.3) the proof of Theorem 3.1. In Section A.1.2, we state and prove Lemmas A.1-A 3,. which completes the proof of (3.9).…”

mentioning

confidence: 99%

Of copulas, quantiles, ranks and spectra: An $L_{1}$-approach to spectral analysis

Dette¹,

Hallin²,

Kley³

et al. 2015

Bernoulli

106

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In this paper, we present an alternative method for the spectral analysis of a univariate, strictly stationary time series {Yt} t∈Z . We define a "new" spectrum as the Fourier transform of the differences between copulas of the pairs (Yt, Y t−k ) and the independence copula. This object is called a copula spectral density kernel and allows to separate the marginal and serial aspects of a time series. We show that this spectrum is closely related to the concept of quantile regression. Like quantile regression, which provides much more information about conditional distributions than classical location-scale regression models, copula spectral density kernels are more informative than traditional spectral densities obtained from classical autocovariances. In particular, copula spectral density kernels, in their population versions, provide (asymptotically provide, in their sample versions) a complete description of the copulas of all pairs (Yt, Y t−k ). Moreover, they inherit the robustness properties of classical quantile regression, and do not require any distributional assumptions such as the existence of finite moments. In order to estimate the copula spectral density kernel, we introduce rank-based Laplace periodograms which are calculated as bilinear forms of weighted L1-projections of the ranks of the observed time series onto a harmonic regression model. We establish the asymptotic distribution of those periodograms, and the consistency of adequately smoothed versions. The finite-sample properties of the new methodology, and its potential for applications are briefly investigated by simulations and a short empirical example.

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A bootstrap test for time series linearity

Cited by 25 publications

References 65 publications

Measuring stationarity in long-memory processes

Measuring stationarity in long-memory processes

Detection of Multiple Structural Breaks in Multivariate Time Series

Of copulas, quantiles, ranks and spectra: An $L_{1}$-approach to spectral analysis

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