Efficient estimation of time-varying parameter models with stochastic volatility

This paper develops an efficient estimation procedure for time-varying parameter autoregressive models with stochastic volatility. Necessary restrictions are imposed on the time-varying autoregressive parameters, thus stability conditions are satisfied. We show that a conditional Gaussian likelihood representation is available with marginalization of linear latent states, thus only non-linear states need to be simulated. The sampling is based on a multivariate extension of the Numerically Accelerated Importance Sampling together with a Rao Blackwellization step to construct a highly efficient maximum likelihood estimator. A simulation study highlights the precision of the procedure in the joint estimation of parameters and latent states. The models are applied to the analysis of inflation dynamics. Estimates of the time-varying parameters indicate the importance of the random innovations in explaining the inflation process, while the trend component is more stable than previously found in the literature. An out-of sample forecasting exercise showed superior results with respect to several benchmark models, especially for long-term forecasting.