Research on Nemerical Methods in Time Series Analysis

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Nonlinear non-Gaussian state space model based time series analysis method was investigated. In particular, Monte Carlo filter and smoother for the state estimation of the nonlinear non-Gaussian state space model was developed. As a result of this research, it became possible to model high-dimensional nonlinear non-Gaussian systems. We also developes a Monte Carlo posterior mean smoother in which almost all particles converge to the mean value of the marginal posterior distribution. These newly developed methods were successfully applied to the development of new statistical analysis method, such as the seasonal adjustment of economic time series, analysis of quasi-periodic motion of data obtained from a satelite and the analysis of a count data.Taking into account of the similarity between Monte Carlo filter and Genetic Algorithm, Higuchi developed a new algorithm for filtering nonlinear non-Gaussian state space model.During the course of this research, a new clew for further deveropment was obtained. In the state space modeling, we used to apply numerical optimization method to estimate the parameters of the model. In this method, evaluation of the likelihoods for many times was required and it sometimes make the estimation very difficult.In view of the fact that our Monte Carlo filter can be applied to high-dimensional nonlinear system, we augmented the state vector with the unknown parameter. With this modification of the state vector it now became possible to estimate the unknown state and the parameter of the model simultaneously. Based on this idea we were lead to develop a self-tuning time series model which has an ability to adjust its unknown parameters automatically.