Research of Parameter Estimation of the State Space Model and its Applications

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In the area of time series analysis, a unified method based on the state space model is frequently used. Recently, in relation to various important real world problems, the necessity of nonlinear or non-Gaussian modeling is recognized. Since the famous Kalman filter cannot yiled efficient state estiamtes, the development of filtering and smoothing algorithms which can be applied to general state space models is very important. The main investigator of this research project developed the non-Gaussian filter/smoother in 1987 and, recently, the Monte Carlo filter which can be aplied high-dimensional general state space model. In this research, we developed a method of simultaneous estiamtion of the stae and the parametors based on these methods.In [1] (in the research report), Kitagawa summarized the entire development of state and parameter estimation for nonlinear non-Gaussian state space modelsand simultaneous estimation by self-organizing state space model. In [2], Kawasaki et al. proposed a method of mitigating the difficulty which arises when the dimension of the observation is by far higher than that of state dimension. In [3], Higuchi proposed a method of seasonal adjustment of small count data. In [4], Kitagawa extended the method of self-organizing filter and developed a method of automatically identify even the noise distribution of the model from the innovation series.The model and numerical computation methods developed in the research were applied to various problems such as finance, economics and earth science. The research report includes some results on the estimation of volatility of finacial data and automatic analysis of GPS data.