Estimating and testing skewness in a stochastic volatility model

In this paper we propose a novel approach to estimating and testing skewness in a stochastic volatility (SV) model. Our key idea is to replace a normal return error in the standard SV model with a split normal error. We show that this simple variation in the model brings about two large computational advantages. First, the stochastic volatility process can be simulated fast and efficiently using a one-block Gibbs sampling technique. Second, more importantly, this is the first to provide a marginal likelihood calculation method to formally test the coexistence of stochastic volatility and skewness in return errors within a Bayesian framework. We demonstrate the efficiency and reliability of our posterior sampling and model comparison methods through a simulation study. The simulation results show that neglecting skewness leads to inaccurate estimates on both the volatility process and conditional expected returns. Our empirical applications to daily stock return data provide a strong evidence of negative skewness.