Bayesian Analysis of Stochastic Volatility Model and Quantile Regression Using Asymmetric Laplace Error via Scale-Mixture of Uniforms

Abstract:

This work considers a Bayesian analysis of stochastic volatility (SV) models using an asymmetric Laplace distribution (ALD) for return. The skewness parameter with the value on (0, 1) of the ALD interval allows us to specify two models under the same distribution but two different estimation techniques. Firstly, if we estimate the skewness parameter, our model is SV model with ALD for return error where the estimated skewness parameter indicates the level of asymmetry or skewness. Secondly, if we fix the skewness parameter at each specified quantile level, our model becomes a quantile SV model. To simplify the estimation algorithm, we construct the ALD through the scale mixture of uniform and gamma distributions. We apply our two models and methods to the return data of five international stock markets including Australia, Hong Kong, Japan, Thailand, and U.K. We find that all returns in five markets during 2000-2010 are slightly skewed and their movements are significantly and positively related to the return in the U.S. market at all quantile levels.