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Statistica Sinica 15(2005), 495-504





ON TIME-REVERSIBILITY OF MULTIVARIATE

LINEAR PROCESSES


Howell Tong$^{1,2}$ and Zhiqiang Zhang$^{1,3}$


$^1$University of Hong Kong, $^2$London School of Economics
and $^3$East China Normal University


Abstract: We study the time-reversibility of multivariate linear processes, introducing a necessary and sufficient condition related to linear transforms of the multivariate linear process. Conditions analogous to Cheng's for univariate non-Gaussian linear processes are also explored; these are in terms of the noise distribution and the model parameters. The exploration results in an easily verifiable set of necessary and sufficient conditions for a multivariate non-Gaussian linear process driven by a univariate noise, leaving the case of multivariate noise as a challenging open problem.



Key words and phrases: Moving average, multivariate linear process, time-reversibility.



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