Bayesian inference for a mixture double autoregressive model

This paper considers a mixture double autoregressive model with two components, which can flexibly capture the features usually exhibited by many financial returns such as heteroscedasticity, large kurtosis and multimodal marginals. Bayesian method based on modern Markov Chain Monte Carlo (MCMC) technology is used to estimate the model parameters. The heteroscedasticity test problem for the underlying process is also addressed by means of Bayes factor. The performances of the proposed methods are evaluated via some simulations. It is shown that the MCMC algorithm is an effective tool to deal with the mixture model. Finally, the proposed model is applied to the S&P500 index data.set.