Bayesian mixture autoregressive model with Student's t innovations

TL;DR

This paper presents a Bayesian mixture autoregressive model incorporating Student's t innovations, offering enhanced tail behavior modeling, fewer parameters, and integrated degrees of freedom estimation for improved flexibility and interpretability.

Contribution

It introduces a fully Bayesian framework for Student's t mixture autoregressive models, including degrees of freedom as estimable parameters, advancing the modeling of heavy-tailed time series.

Findings

Model captures tail behavior more effectively than Gaussian models.

Fitted models require fewer parameters.

Degrees of freedom are estimated within the Bayesian framework.

Abstract

This paper introduces a fully Bayesian analysis of mixture autoregressive models with Student t components. With the capacity of capturing the behaviour in the tails of the distribution, the Student t MAR model provides a more flexible modelling framework than its Gaussian counterpart, leading to fitted models with fewer parameters and of easier interpretation. The degrees of freedom are also treated as random variables, and hence are included in the estimation process.