MIXTURE-MODELS FOR TIME-SERIES

In this paper we extend the class of zero-order threshold autoregressi ve models to a much richer class of mixture models. The new class has the important property of duality which, as we show, corresponds to ti me reversal. We are then able to obtain the time reversals of the zero -order threshold models and to characterise the time-reversible member s of this subclass. These turn out to be quite trivial. The time-rever sible models of the more general class do not suffer in this way. The complete stationary distributional structure is given, as are various moments, in particular the autocovariance function. This is shown to b e of ARMA type. Finally we give two examples, the second of which exte nds from the finite to the countable mixture case. The general theory for this extension will be given elsewhere.