Numerical integration-based Gaussian mixture filters for maximum likelihood estimation of asymmetric stochastic volatility models

I consider Gaussian filters based on numerical integration for maximum likelihood estimation of stochastic volatility models with leverage. I show that for this class of models, the prediction step of the Gaussian filter can be evaluated analytically without linearizing the state--space model. Monte Carlo simulations show that the mixture Gaussian filter performs remarkably well in terms of both accuracy and computation time compared to the quasi-maximum likelihood and importance sampler filters. The result that the prediction step of the Gaussian filter can be evaluated analytically is shown to apply more generally to a number of commonly used specifications of the stochastic volatility model. Copyright Royal Economic Society 2007