Bayesian collapsed Gibbs sampling for a stochastic volatility model with a Dirichlet process mixture

This paper replicates the results of the stochastic volatility-Dirichlet process mixture (SV-DPM) models proposed in Jensen and Maheu (2010) in both a narrow and a wide sense. By using a normal-Wishart prior and the collapsed Gibbs sampling method, our algorithm can be applied for more general settings, and it is more efficient for sampling the Dirichlet process mixture. For the stochastic volatility component, we adopt the method in Chan (2017) to further increase the overall efficiency of our algorithm. Using the same dataset, we obtain mixed results. Some of the results have significant differences. If we use recent time period dataset, which includes the COVID-19 pandemic period, the log market portfolio volatility seems to increase in terms of the number of clusters and size of magnitude.