Volatility or higher moments: Which is more important in return density forecasts of stochastic volatility model?

The stochastic volatility (SV) model has been one of the most popular models for latent stock return volatility. Extensions of the SV model focus on either improving volatility inference or modeling higher moments of the return distribution. This study investigates which extension can better improve return density forecasts. By examining various specifications with S&P 500 daily returns for nearly 20 years, we find that a more accurate capture of volatility dynamics with realized volatility and implied volatility is more important than modeling higher moments for a conventional SV model in terms of both density and tail forecasts. The accuracy of volatility estimation and forecasts should be the precondition for higher moments extensions