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

2021/02/26 by Luis E. Nieto‐Barajas, Luis Nieto-Barajas, Nieto-Barajas, Luis +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.2103.01218

openalex publication_date 2021/02/26 · arxiv created 2021/10/14 · arxiv updated 2021/10/15 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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.

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• Graphical models with marginals in the exponential family

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