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This paper deals with the filtering problem for a class of discrete timestochastic volatility models in which the disturbances have rationalprobability density functions. This includes the Cauchy distributions andStudent t-distributions with odd number of degrees of freedom. Using statespace realizations to represent the rational probability density functions weare able to solve the filtering problem exactly. However the size of theinvolved state space matrices grows exponentially with each time step of thefilter. Therefore we use stochastically balanced truncation techniques toapproximate the high order rational functions involved. In a simulation studywe show the applicability of this approach. In addition a simple method ofmoments estimator is derived.

Filtering and estimation in stochastic volatility models with rationally distributed disturbances