Multivariate lag-windows and group representations

Berg, Arthur

doi:10.1016/j.jmva.2008.02.038

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Bispectrum1

Estimation Of the Normalized Bispectrum1

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2010

2023

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Cited by 4 publications

(2 citation statements)

References 26 publications

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“…It is worth noting that the symmetrized version of λ is connected to the theory of group representations of the symmetric group S 3 ; see Berg (2006) for more details. Several choices of lag-windows are considered in Subba Rao and Terdik (2003) including the so-called "optimal window", λ opt , which is in some sense optimal among lag-windows of order 2; refer to Theorem 2 on page 43 of Subba Rao and Gabr (1984).…”

Section: Bispectrummentioning

confidence: 99%

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

Berg

Politis

2007

Ann Inst Stat Math

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Section: Bispectrummentioning

confidence: 99%

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

Berg

Politis

2007

Ann Inst Stat Math

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“…However, just like we do not wish to have variance estimates to be negative, conditions in (7) should be imposed in practice; techniques given in Berg (2008) can be used to symmetrize any function w(·) or w(·, ·) to satisfy (7).…”

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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