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

TL;DR

This paper presents a method to create complex dependence structures among random variables with invariant marginals from conjugate exponential families with quadratic variance functions, applicable to various models including spatial and temporal data.

Contribution

It introduces a novel procedure to induce diverse dependence structures using latent variables linked to conjugate exponential families with quadratic variance functions.

Findings

Allows modeling of order-q moving average and seasonal dependencies

Enables strict stationarity in the constructed models

Applicable to spatial and spatio-temporal data

Abstract

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, spatial and spatio-temporal dependences. The invariant marginal distribution can be in any family that is conjugate to an exponential family with quadratic variance function. Dependence is induced via a set of suitable 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.