Abstract
Computing statistics approach to time series analysis is shown. Various important problems in time series analysis such as prediction, interpolation, decomposition and the parameter estimation can be unified as the state estimation problem of a properly defined state space model. For the standard linear Gaussian state space models, the state estimation can be achieved very efficiently by the famous Kalman filter and fixed interval smoothing algorithms. By intensive use of computers, a similar recursive computation for very general nonlinear non-Gaussian state space model can be developed. In this paper, numerical methods based on numerical integration and Monte Carlo approximation are shown. A self-organizing state space model for simultaneous estimation of the state parameters and the structural parameters is also shown. As numerical examples, estimation of changing volatilities of seismic data and stock price data are considered.
