Stochastic volatility with heterogeneous time scales

In this work, the model for the statistical description of financial stylized facts proposed in Delpini and Bormetti (2011) is amended from the unrealistically fast decay of the volatility autocorrelation. This is achieved by introducing an extra stochastic factor that drives the volatility. With respect to previous approaches and analyses of continuous-time stochastic volatility models, we believe that the estimation procedure proposed here represents a further improvement and fulfills the desirable requirements of statistical soundness. At the same time, it also allows us to focus on those facts which are established as relevant for the description of financial data. In particular, we pursue an heuristic approach to optimization that reduces the dimensionality of the parameter space and retains only the ingredients needed to capture the aforementioned empirical evidence.