NONLINEAR AND NON-GAUSSIAN STATE SPACE MODELING USING SAMPLING TECHNIQUES

HISASHI TANIZAKI

Faculty of Economics, Kobe University, Kobe 657-5801, Japan, e-mail: tanizaki@kobe-u.ac.jp

(Received April 11, 2000; revised October 12, 2000)

Abstract. In this paper, the nonlinear non-Gaussian filters and smoothers are proposed using the joint density of the state variables, where the sampling techniques such as rejection sampling (RS), importance resampling (IR) and the Metropolis-Hastings independence sampling (MH) are utilized. Utilizing the random draws generated from the joint density, the density-based recursive algorithms on filtering and smoothing can be obtained. Furthermore, taking into account possibility of structural changes and outliers during the estimation period, the appropriately chosen sampling density is possibly introduced into the suggested nonlinear non-Gaussian filtering and smoothing procedures. Finally, through Monte Carlo simulation studies, the suggested filters and smoothers are examined.

Key words and phrases: Filtering, smoothing, joint density, rejection sampling, importance resampling, Metropolis-Hastings independence sampling.