Before revision: We compare the predictive ability of several volatility models for a long series of weekly log-returns of the Dow Jones Industrial Average Index from 1902 to 2016. Our focus is particularly on predicting one and multi-step ahead conditional and aggregated conditional densities. Our set of competing models includes: Well-known GARCH specifications, Markov switching GARCH, sempiparametric GARCH, Generalised Autoregressive Score (GAS), the plain stochastic volatility (SV) as well as its more flexible extensions such as SV with leverage, in-mean effects and Student-t distributed errors .
After revision: The leverage effect refers to the well-established relationship between returns and volatility. When returns fall, volatility increases. We examine the role of the leverage effect with regards to generating density forecasts of equity returns using well-known observation and parameter-driven volatility models. These models differ in their assumptions regarding: The parametric specification, the evolution of the conditional volatility process and how the leverage effect is accounted for. The ability of a model to generate accurate density forecasts when the leverage effect is incorporated or not as well as its more flexible extensions such as SV with leverage, in-mean effects and Student-t distributed errors .