Multivariate Lag-Windows and Group Representations

Details Multivariate Lag-Windows and Group Representations Multivariate Lag-Windows and Group Representations

2006-12-22

arxiv.org/abs/math/0612674v1

Mathematics

Statistics Theory

19 pages, 3 figures

Scientific paper

Symmetries of the auto-cumulant function (the 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 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, used to estimate general kth-order spectra, is also derived through the developed theory.

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