Modelling financial time series based on heavy-tailed market microstructure models with scale mixtures of normal distributions |
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Authors: | Yanhui Xi Hui Peng |
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Affiliation: | 1. Hunan Province Higher Education Key Laboratory of Power System Safety Operation and Control, Changsha University of Science and Technology , Changsha, Hunan, China;2. School of Information Science &3. Engineering, Central South University, Changsha, Hunan, China |
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Abstract: | 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. |
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Keywords: | Market microstructure model scale mixtures of normal distributions heavy tail outlier Markov Chain Monte Carlo |
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