Abstract: A nonlinear state space approach to the smoothing of time series is shown. The time series is expressed in state space model form where the system model or the observation model contains nonlinear functions of the state vector. Recursive formulas of prediction, filtering and smoothing for the nonlinear state space model are given. Numerical implementation of the formula is shown based on numerical approximation to the densities and numerical computation for the nonlinear transformation of variables, convolution of two densities, Bayes formula, and normalization. Significant merits of nonlinear state space modeling and of the proposed smoother are illustrated by two numerical examples. Empirical study on the numerical accuracy was also performed on one of the examples.
Key words and phrases: Filtering, smoothing, likelihood, AIC, nonlinear model, non-Gaussian distribution.