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
Issue number10
StatePublished - Nov 2008

All Science Journal Classification (ASJC) codes

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


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