Modelling financial time series based on heavy-tailed market microstructure models with scale mixtures of normal distributions

This paper presents a type of heavy-tailed market microstructure models with the scale mixtures of normal distributions (MM-SMN), which include two specific sub-classes, viz. the slash and the Student-t distributions. Under a Bayesian perspective, the Markov Chain Monte Carlo (MCMC) method is constructed to estimate all the parameters and latent variables in the proposed MM-SMN models. Two evaluating indices, namely the deviance information criterion (DIC) and the test of white noise hypothesis on the standardised residual, are used to compare the MM-SMN models with the classic normal market microstructure (MM-N) model and the stochastic volatility models with the scale mixtures of normal distributions (SV-SMN). Empirical studies on daily stock return data show that the MM-SMN models can accommodate possible outliers in the observed returns by use of the mixing latent variable. These results also indicate that the heavy-tailed MM-SMN models have better model fitting than the MM-N model, and the market microstructure model with slash distribution (MM-s) has the best model fitting. Finally, the two evaluating indices indicate that the market microstructure models with three different distributions are superior to the corresponding stochastic volatility models.