Time-reversibility is defined for a process X ( t ) as the property that { X ( t 1 ), …, X ( t n )} and { X (– t 1 ), …, X (– t n )} have the same joint probability distribution. It is shown that, for discrete mixed autoregressive moving-average processes, this is a unique property of Gaussian processes.
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Gideon Weiss (1975) studied this question.