Elliott, R.Siu, T.Fung, E.2012-03-212012-03-212012Nonlinear Dynamics, 2012; 67(2):1295-13130924-090X1573-269Xhttp://hdl.handle.net/2440/69983We introduce a class of stochastic volatility models whose parameters are modulated by a hidden nonlinear dynamical system. Our aim is to incorporate the impact of economic cycles, or business cycles, into the long-term behavior of volatility dynamics. We develop a discrete-time nonlinear filter for the estimation of the hidden volatility and the nonlinear dynamical system based on return observations. By exploiting the technique of a reference probability measure we derive filters for the hidden volatility and the nonlinear dynamical system.en© Springer Science+Business Media B.V. 2011Stochastic volatilityNonlinear dynamical systemEconomic cyclesNonlinear filtersChange of measuresReference probabilityJournal article002011550810.1007/s11071-011-0069-40002978201000312-s2.0-8485575701826404