A Semiparametric Stochastic Volatility Model with Dependent Errors

Abstract: This paper proposes a semiparametric stochastic volatility (SV) model that relaxes the restrictive Gaussian assumption in both the return and volatility error terms, allowing them to follow flexible, nonparametric distributions with potential dependence. By integrating this framework into a Bayesian Markov Chain Monte Carlo (MCMC) approach, the model effectively captures the heavy tails, skewness, and other complex features often observed in financial return data. Simulation studies under correlated Gaussian and Student's t error settings demonstrate that the proposed method achieves lower bias and variance when estimating model parameters and volatility compared to traditional Gaussian-based and popular Bayesian implementations. We conduct an empirical application to the real world financial data, which further underscores the model's practical advantages: it provides volatility estimates that respond more accurately to large fluctuations, reflecting real-world market behavior. These findings suggest that the introduced semiparametric SV framework offers a more robust and adaptable tool for financial econometrics, particularly in scenarios characterized by non-Gaussian and dependent return dynamics.