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

We describe a procedure to introduce general dependence structures on a set\nof random variables. These include order-$q$ moving average-type structures, as\nwell as seasonal, periodic, spatial and spatio-temporal dependences. The\ninvariant marginal distribution can be in any family that is conjugate to an\nexponential family with quadratic variance function. Dependence is induced via\na set of suitable latent variables whose conditional distribution mirrors the\nsampling distribution in a Bayesian conjugate analysis of such exponential\nfamilies. We obtain strict stationarity as a special case.\n