A note on time-reversibility of multivariate linear processes

Kung-Sik Chan, Lop-Hing Ho and Howell Tong

Biometrika, 2006, vol. 93, issue 1, 221-227

Abstract: We derive some readily verifiable necessary and sufficient conditions for a multivariate non-Gaussian linear process to be time-reversible, under two sets of conditions on the contemporaneous dependence structure of the innovations. One set of conditions concerns the case of independent-component innovations, in which case a multivariate non-Gaussian linear process is time-reversible if and only if the coefficients consist of essentially asymmetric columns with column-specific origins of symmetry or symmetric pairs of columns with pair-specific origins of symmetry. On the other hand, for dependent-component innovations plus other regularity conditions, a multivariate non-Gaussian linear process is time-reversible if and only if the coefficients are essentially symmetric about some origin. Copyright 2006, Oxford University Press.

Date: 2006
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