  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.
