The article discusses how stochastic volatility models are more complex to estimate than other models. The researchers show how to efficiently estimate and predict different types of these models, including ones with fat-tailed and skewed distributions. They also explore models with correlated errors and multivariate models. By using a hierarchy of conditional probability distributions, they can create more realistic models. Their approach involves simulating the joint distribution of volatilities and parameters using MCMC methods. The researchers find that these extensions are necessary when modeling financial time series, as they discover evidence of non-normal distributions and correlated errors in stock returns and exchange rates.