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.
Highlights
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
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
Mixture autoregressive (MAR) models (Wong and Li 2000) provide a flexible way to model time series with predictive distributions which depend on the recent history of the process
Summary
Mixture autoregressive (MAR) models (Wong and Li 2000) provide a flexible way to model time series with predictive distributions which depend on the recent history of the process. Reversible jump MCMC (Green 1995) is used to select the autoregressive orders of the components in the mixture, and models with different number of components are compared using methods by Chib (1995) and Chib and Jeliazkov (2001), which exploit the marginal likelihood identity. He derives analytically posterior distributions for all parameters in the selected model.
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