Practical filtering for stochastic volatility models

This paper provides a simulation-based approach to filtering and sequential parameter learning for stochastic volatility models. We develop a fast simulation-based approach using the practical filter of Polson, Stroud and Müller (2002). We compare our approach to sequential parameter learning and filtering with an auxiliary particle filtering algorithm based on Storvik (2002). For simulated data, there is close agreement between the two methods. For data on the S&P 500 market stock index from 1984–90, our algorithm agrees closely with a full MCMC analysis, whereas the auxiliary particle filter degenerates. State Space and Unobserved Component Models: Theory and Applications, eds. Andrew C. Harvey, Siem Jan Koopman and Neil Shephard. Published by Cambridge University Press. C © Cambridge University Press 2004