Smooth and Nonparametric Filtering for Likelihood Inference in Dynamic Latent Variables Models
Christian Brownlees (UPF)
Abstract: This paper proposes novel Sequential Monte Carlo (SMC) methods for maximum likelihood estimation of dynamic latent variable models (DLVM). Our proposal has two highlights. Contrary to most traditional SMC algorithms, our technique delivers likelihood approximations that are smooth with respect to the underlying parameter, hence suitable for maximum likelihood estimation. Moreover, the method is suitable for the estimation of markov models with latent components where the measurement density is not available in closed form but it is still possible to simulate from the transition density. This is useful, for instance, in the estimation of continuous time stochastic volatility models where the measurement density is not available in general. We establish rate results for the filter and establish the asymptotic properties of the resulting estimators. The usefulness of the methodology is illustrated with Monte Carlo studies and an application to the estimation of continuous-time stochastic volatility models given first-step estimates of integrated volatility.
Monday 19th March 2012, 13:00 - 14:00, W316
Abstract: This paper proposes novel Sequential Monte Carlo (SMC) methods for maximum likelihood estimation of dynamic latent variable models (DLVM). Our proposal has two highlights. Contrary to most traditional SMC algorithms, our technique delivers likelihood approximations that are smooth with respect to the underlying parameter, hence suitable for maximum likelihood estimation. Moreover, the method is suitable for the estimation of markov models with latent components where the measurement density is not available in closed form but it is still possible to simulate from the transition density. This is useful, for instance, in the estimation of continuous time stochastic volatility models where the measurement density is not available in general. We establish rate results for the filter and establish the asymptotic properties of the resulting estimators. The usefulness of the methodology is illustrated with Monte Carlo studies and an application to the estimation of continuous-time stochastic volatility models given first-step estimates of integrated volatility.
Monday 19th March 2012, 13:00 - 14:00, W316