Bayesian inference for nonlinear structural time series models

This article discusses a partially adapted particle filter for estimating the likelihood of a nonlinear structural econometric state space models whose state transition density cannot be expressed in closed form. The filter generates the disturbances in the state transition equation and allows for multiple modes in the conditional disturbance distribution. The particle filter produces an unbiased estimate of the likelihood and so can be used to carry out Bayesian inference in a particle Markov chain Monte Carlo framework. We show empirically that when the signal to noise ratio is high, the new filter can be much more efficient than the standard particle filter, in the sense that it requires far fewer particles to give the same accuracy. The new filter is applied to several simulated and real examples and in particular to a dynamic stochastic general equilibrium model.