Higher-order accurate polyspectral estimation with flat-top lag-windows

Berg, Arthur; Politis, Dimitris N.

doi:10.1007/s10463-007-0154-0

Cited by 8 publications

(13 citation statements)

References 16 publications

(17 reference statements)

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“…The case j = k of the theorem was first given in Politis (2003) for the trapezoidal flat-top kernel; a similar theorem is also given in Berg and Politis (2008). It is important to note that the theorem is valid even under the settting of Section 3, i.e., under a potential lack of finite fourth moments.…”

Section: Adaptive Bandwidth Choicementioning

confidence: 80%

“…There is no inherent discrepancy between the notion of flat-top kernels and "fixed-b" 7 asymptotics. 4 Indeed, the latter could-in principle-be used in connection with flat-top kernels but it seems that the improvements will be marginal (if at all). The reason is that for small bandwidths, the "fixed-b" asymptotics coincide with the traditional approximations, and that flat-top kernels are characterized by small (even ultra-small) optimal bandwidths; see e.g.…”

Section: Theorem 21 Assume Conditions Strong Enough To Ensure Thatmentioning

confidence: 99%

“…The corresponding flat-top kernel estimator of f isf with (j, k) element given 4 The "steep-origin" kernels of Phillips, Sun, and Jin (2006) are competitors to the "fixed-b" asymptotics but the underlying idea is the same, i.e., better approximations when the bandwidth happens to be large;…”

Section: Spectral Estimation In the Absence Of Finite Fourth Momentsmentioning

confidence: 99%

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Higher-Order Accurate, Positive Semidefinite Estimation of Large-Sample Covariance and Spectral Density Matrices

2011

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A new class of large-sample covariance and spectral density matrix estimators is proposed based on the notion of flat-top kernels. The new estimators are shown to be higher-order accurate when higher-order accuracy is possible. A discussion on kernel choice is presented as well as a supporting finite-sample simulation. The problem of spectral estimation under a potential lack of finite fourth moments is also addressed.The higher-order accuracy of flat-top kernel estimators typically comes at the sacrifice of the positive semi-definite property. Nevertheless, we show how a flat-top estimator can be modified to become positive semi-definite (even strictly positive definite) while maintaining its higher-order accuracy. In addition, an easy (and consistent) procedure for optimal bandwidth choice is given; this procedure estimates the optimal bandwidth associated with each individual element of the target matrix, automatically sensing (and adapting to) the underlying correlation structure. * Research partially supported by NSF grants SES-04-18136 and DMS-07-06732. Many thanks are due to Arthur Berg and Tucker McElroy for numerous helpful interventions, to Peter Robinson for a critical reading and suggestions of some key early references, and to Dimitrios Gatzouras for his help with the proof of Lemma 10.1. The S+ software for the practical computation of the different spectral density estimators was compiled with the invaluable help of Isheeta Nargis and Arif Dowla of www.stochasticlogic.com, and is now publicly available from: www.math.ucsd.edu/∼politis/SOFT/SfunctionsFLAT-TOPS.html.

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Section: Adaptive Bandwidth Choicementioning

confidence: 80%

Section: Theorem 21 Assume Conditions Strong Enough To Ensure Thatmentioning

confidence: 99%

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Higher-Order Accurate, Positive Semidefinite Estimation of Large-Sample Covariance and Spectral Density Matrices

2011

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“…In practice, when the data are not assumed to have mean zero, X t would be centered to the sample mean; such data-based centering does not spoil the asymptotic results-cf. Berg and Politis (2009). Kernel estimators of the spectrum and bispectrum are given by (Parzen, 1957;Rosenblatt and Van Ness, 1965;Grenander and Rosenblatt, 1984) f (λ) = 1 2π…”

Section: Estimation Of the Normalized Bispectrummentioning

confidence: 99%

“…The flat-top lag window functions form a class of functions for w(·) and w(·, ·) with infinite characteristic exponent that possess certain mean-square error optimality properties (Politis and Romano, 1995;Berg and Politis, 2009;Politis, 2009); these functions do not have compact support, but do satisfy sufficient criteria such as…”

Section: Estimation Of the Normalized Bispectrummentioning

confidence: 99%

A bootstrap test for time series linearity

Berg

Paparoditis

Politis

2010

Journal of Statistical Planning and Inference

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A bootstrap algorithm is proposed for testing Gaussianity and linearity in stationary time series, and consistency of the relevant bootstrap approximations is proven rigorously for the first time. Subba Rao and Gabr (1980) and Hinich (1982) have formulated some well-known nonparametric tests for Gaussianity and linearity based on the asymptotic distribution of the normalized bispectrum. The proposed bootstrap procedure gives an alternative way to approximate the finite-sample null distribution of such test statistics. We revisit a modified form of Hinich's test utilizing kernel smoothing, and compare its performance to the bootstrap test on several simulated and two real data sets-the S&P 500 returns and the quarterly US real GNP growth rate. Interestingly, Hinich's test and the proposed bootstrapped version yield substantially different results when testing Gaussianity and linearity of the GNP data.

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T-Moments and T-Cumulants

Terdik

2021

Multivariate Statistical Methods

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Higher-order accurate polyspectral estimation with flat-top lag-windows

Abstract: Bispectrum, Nonparametric estimation, Spectral density, Time series,

Cited by 8 publications

References 16 publications

Higher-Order Accurate, Positive Semidefinite Estimation of Large-Sample Covariance and Spectral Density Matrices

Higher-Order Accurate, Positive Semidefinite Estimation of Large-Sample Covariance and Spectral Density Matrices

A bootstrap test for time series linearity

T-Moments and T-Cumulants

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