General dependence structures for some models based on exponential families with quadratic variance functions

02/26/2021

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by   Luis Nieto-Barajas, et al.

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We describe a procedure to introduce general dependence structures on a set of random variables. These include order-q moving average-type structures, as well as seasonal, periodic and spatial dependences. The invariant marginal distribution can be in any family that is conjugate to an exponential family with quadratic variance functions. Dependence is induced via latent variables whose conditional distribution mirrors the sampling distribution in a Bayesian conjugate analysis of such exponential families. We obtain strict stationarity as a special case.