Bayesian analysis of mixture autoregressive models covering the complete parameter space

TL;DR

This paper introduces a novel Bayesian sampling method for mixture autoregressive models that effectively explores the entire parameter space and addresses label switching, enhancing predictive accuracy for complex time series.

Contribution

A new Bayesian sampling approach for MAR models that covers the full parameter space and includes a relabeling algorithm to handle label switching, improving inference accuracy.

Findings

Effective sampling of the complete parameter space.

Improved handling of label switching.

Enhanced density forecasting capabilities.

Abstract

Mixture autoregressive (MAR) models provide a flexible way to model time series with predictive distributions which depend on the recent history of the process and are able to accommodate asymmetry and multimodality. Bayesian inference for such models offers the additional advantage of incorporating the uncertainty in the estimated models into the predictions. We introduce a new way of sampling from the posterior distribution of the parameters of MAR models which allows for covering the complete parameter space of the models, unlike previous approaches. We also propose a relabelling algorithm to deal a posteriori with label switching. We apply our new method to simulated and real datasets, discuss the accuracy and performance of our new method, as well as its advantages over previous studies. The idea of density forecasting using MCMC output is also introduced.