On a spectral density estimate obtained by averaging periodograms

Dahlhaus, Rainer

doi:10.2307/3213863

Cited by 25 publications

(9 citation statements)

References 14 publications

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“…The notion of tapering for time series—especially in connection to spectral estimation—is well‐studied; see, for example, Welch (1967), Brillinger (1975), Priestley (1981), Dahlhaus (1985), Dahlhaus (1990), and Künsch (1989). It is customary to obtain the sequence of data‐tapering windows by means of dilations of a single function w : R → [0, 1], i.e.…”

Section: The Tapered Block Bootstrap For Approximately Linear Statisticsmentioning

confidence: 99%

“…In connection with the closely related problem of spectral estimation, many different choices for tapering windows have been discussed in the literature; cf. Welch (1967), Brillinger (1975), Priestley (1981), Dahlhaus (1985), and Künsch (1989). Zhurbenko (1986, p. 123) mentions some optimality properties of the Kolmogorov–Zhurbenko window but the construction of this window is very cumbersome; in addition, Dahlhaus (1985) shows that the simpler Tukey–Hanning window has quite comparable performance.…”

Section: Choosing the Shape Of The Tapering Windowmentioning

confidence: 99%

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The tapered block bootstrap for general statistics from stationary sequences

Paparoditis

Politis

2002

The Econometrics Journal

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In this paper, we define and study a new block bootstrap variation, the taper ed block bootstrap, that is applicable in the general case of approximately linear statistics, and constitutes an improvement over the original block bootstrap of Künsch (1989). The asymptotic validity, and the favorable bias properties of the tapered block bootstrap are shown in two important cases: smooth functions of means, and M-estimators. The important practical issues of optimally choosing the window shape and the block size are addressed in detail, while some finite-sample simulations are also presented.

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Section: The Tapered Block Bootstrap For Approximately Linear Statisticsmentioning

confidence: 99%

Section: Choosing the Shape Of The Tapering Windowmentioning

confidence: 99%

The tapered block bootstrap for general statistics from stationary sequences

Paparoditis

Politis

2002

The Econometrics Journal

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“…Hence, Γ can be obtained from Σ by replacing ϕ k (•) with ϕ k (− •), and we stated the explicit form merely for convenience reasons. We refer to Rosenblatt (1963), Brillinger (1981), Dahlhaus (1985) and Taniguchi and Kakizawa (2000).…”

Section: Preliminaries and Basic Resultsmentioning

confidence: 99%

Extending the validity of frequency domain bootstrap methods to general stationary processes

Meyer¹,

Paparoditis²,

Kreiß³

2020

Ann. Statist.

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For many relevant statistics of multivariate time series, no valid frequency domain bootstrap procedures exist. This is mainly due to the fact that the distribution of such statistics depends on the fourth-order moment structure of the underlying process in nearly every scenario, except for some special cases like Gaussian time series. In contrast to the univariate case, even additional structural assumptions such as linearity of the multivariate process or a standardization of the statistic of interest do not solve the problem. This paper focuses on integrated periodogram statistics as well as functions thereof and presents a new frequency domain bootstrap procedure for multivariate time series, the multivariate frequency domain hybrid bootstrap (MFHB), to fill this gap. Asymptotic validity of the MFHB procedure is established for general classes of periodogram-based statistics and for stationary multivariate processes satisfying rather weak dependence conditions. A simulation study is carried out which compares the finite sample performance of the MFHB with that of the moving block bootstrap.

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“…(iv) Note that the rescaling quantity f b used in ( 2) is actually itself a spectral density estimator which is based on averaging periodograms calculated over subsamples. Such estimators have been thoroughly investigated by many authors in the literature; Bartlett (1948Bartlett ( ), (1950, Welch (1967); see also Dahlhaus (1985). We will make use of some of the results obtained for this estimator later on.…”

Section: Convolved Bootstrapped Periodograms Of Subsamplesmentioning

confidence: 99%

A Frequency Domain Bootstrap for General Stationary Processes

Meyer,

Paparoditis,

Kreiss

2018

Preprint

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Existing frequency domain methods for bootstrapping time series have a limited range. Consider for instance the class of spectral mean statistics (also called integrated periodograms) which includes many important statistics in time series analysis, such as sample autocovariances and autocorrelations among other things. Essentially, such frequency domain bootstrap procedures cover the case of linear time series with independent innovations, and some even require the time series to be Gaussian. In this paper we propose a new, frequency domain bootstrap method which is consistent for a much wider range of stationary processes and can be applied to a large class of periodogram-based statistics. It introduces a new concept of convolved periodograms of smaller samples which uses pseudo periodograms of subsamples generated in a way that correctly imitates the weak dependence structure of the periodogram. We show consistency for this procedure for a general class of stationary time series, ranging clearly beyond linear processes, and for general spectral means and ratio statistics. Furthermore, and for the class of spectral means, we also show, how, using this new approach, existing bootstrap methods, which replicate appropriately only the dominant part of the distribution of interest, can be corrected. The finite sample performance of the new bootstrap procedure is illustrated via simulations.

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On a spectral density estimate obtained by averaging periodograms

Cited by 25 publications

References 14 publications

The tapered block bootstrap for general statistics from stationary sequences

The tapered block bootstrap for general statistics from stationary sequences

Extending the validity of frequency domain bootstrap methods to general stationary processes

A Frequency Domain Bootstrap for General Stationary Processes

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