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We describe a procedure to introduce general dependence structures on a setof random variables. These include order-$q$ moving average-type structures, aswell as seasonal, periodic, spatial and spatio-temporal dependences. Theinvariant marginal distribution can be in any family that is conjugate to anexponential family with quadratic variance function. Dependence is induced viaa set of suitable latent variables whose conditional distribution mirrors thesampling distribution in a Bayesian conjugate analysis of such exponentialfamilies. We obtain strict stationarity as a special case.

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