Bayesian Markov mixture of normals approach to modeling financial returns

Purpose – The purpose of this paper is to investigate whether Markov mixture of normals (MMN) model is a viable approach to modeling financial returns. Design/methodology/approach – This paper adopts the full Bayesian estimation approach based on the method of Gibbs sampling, and the latent state variables simulation algorithm developed by Chib. Findings – Using data from the S&P 500 index, the paper first demonstrates that the MMN model is able to capture the unconditional features of the S&P 500 daily returns. It further conducts formal model comparisons to examine the performance of the Markov mixture structures relative to two well‐known alternatives, the GARCH and the t‐GARCH models. The results clearly indicate that MMN models are viable alternatives to modeling financial returns. Research limitations/implications – The univariate MMN structure in this paper can be generalized to a multivariate setting, which can provide a flexible yet practical approach to modeling multiple time series of assets returns. Practical implications – Given the encouraging empirical performance of the MMN models, it is hopeful that the MMN models will have success in some interesting financial applications such as Value‐at‐Risk and option pricing. Originality/value – The paper explicitly formulates the Gibbs sampling procedures for estimating MMN models in a Bayesian framework. It also shows empirically that MMN models are able to capture the stylized features of financial returns. The MMN models and their estimation method in this paper can be applied to other financial data, especially in which tail probability is of major interest or concern.