On the construction of stationary AR(1) models via random distributions

Abstract

We explore a method for constructing first-order stationary autoregressive-type models with given marginal distributions. We impose the underlying dependence structure in the model using Bayesian non-parametric predictive distributions. This approach allows for nonlinear dependency and at the same time works for any choice of marginal distribution. In particular, we look at the case of discrete-valued models; that is the marginal distributions are supported on the non-negative integers.

Keywords:

• AR model
• Beta-Stacy process
• Bayesian non-parametrics
• discrete-valued time series
• Pólya trees
• stationary process

Acknowledgements

Alberto Contreras-Cristán and Ramsés H. Mena are grateful for the support from PAPIIT grant IN109906 and CONACyT grant J48538, UNAM, México. The research of Stephen G. Walker was partially supported by an EPSRC Advanced Research Fellowship.