Statistica Sinica

Richard A. Davis and Gabriel Rodriguez-Yam

Abstract:Typically, the likelihood function for non-Gaussian state-space models cannot be computed explicitly and simulation-based procedures, such as importance sampling or MCMC, are commonly used to estimate model parameters. In this paper we consider two alternative estimation procedures, each based on an approximation to the likelihood function. In the first approach, the approximation is computed and maximized directly, and this results in a fast estimation procedure without resort to simulation. Moreover, estimates are competitive with those produced using simulation-based procedures. The speed of the procedure makes it viable to fit a wide range of potential models to the data, and it allows for bootstrapping parameter estimates. In the second approach, importance sampling is used to estimate the error in the approximation to the likelihood. This particular simulation-based method is extremely quick and accurate, since the error term is well-approximated by a linear function.

Key words and phrases:Approximate likelihood, importance sampling, non-linear state space models, stochastic volatility models.