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 SV 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 skewness and SV in a Bayesian framework. We subsequently demonstrate the efficiency and reliability of our posterior sampling and model comparison methods through a simulation study. The simulation study results also show that neglecting skewness leads to inaccurate SV estimates and conditional expected returns. Our empirical applications to daily stock return data also show strong evidence of negative skewness.