Abstract

Symmetries of the auto-cumulant function (a generalization of the auto-covariance function) of a kth-order stationary time series are derived through a connection with the symmetric group of degree k. Using the theory of group representations, symmetries of the auto-cumulant function are demystified and lag-window functions are symmetrized to satisfy these symmetries. A generalized Gabr-Rao optimal kernel is also derived through the developed theory.

Original languageEnglish (US)
Pages (from-to)2479-2496
Number of pages18
JournalJournal of Multivariate Analysis
Volume99
Issue number10
DOIs
StatePublished - Nov 1 2008

Fingerprint

Group Representation
Cumulants
Symmetry
Optimal Kernel
Autocovariance Function
Stationary Time Series
Symmetric group
Time series
Lag

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Cite this

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title = "Multivariate lag-windows and group representations",
abstract = "Symmetries of the auto-cumulant function (a generalization of the auto-covariance function) of a kth-order stationary time series are derived through a connection with the symmetric group of degree k. Using the theory of group representations, symmetries of the auto-cumulant function are demystified and lag-window functions are symmetrized to satisfy these symmetries. A generalized Gabr-Rao optimal kernel is also derived through the developed theory.",
author = "Arthur Berg",
year = "2008",
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language = "English (US)",
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Multivariate lag-windows and group representations. / Berg, Arthur.

In: Journal of Multivariate Analysis, Vol. 99, No. 10, 01.11.2008, p. 2479-2496.

Research output: Contribution to journalArticle

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