Stochastic Volatility Systems

Stochastic Volatility models represent a well-known framework for the analysis of nancial time series data, together with the other important class of ARCH-type models. The main diierence between them, at least from a statistical point of view, relies on the possibility of obtaining exact inference, in particular with regard to the estimation issue. While for ARCH-type models the standard results apply, in the sense that Maximum Likelihood estimates for the parameters of interest can be computed, for Stochastic Volatility Models there are more complications and usually only approximate results can be obtained, unless two particular estimation strategies are employed: (a) exact nongaussian ltering methods (b) simulation techniques. In this paper we stress the importance of \ only " approximate and therefore sub-optimal estimation methods for special models whose complexity makes hard the task of nding exact solutions. The setup where the analysis is conducted is the state space formulation and this suggests to enclose the cases here considered in a class of so-called Stochastic Volatility Systems.