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

在时间序列分析领域，常用的是基于状态空间模型的统一方法。近年来，在涉及到各种重要的现实问题时，人们认识到非线性或非高斯建模的必要性。由于著名的卡尔曼滤波不能产生有效的状态估计，因此开发适用于一般状态空间模型的滤波和平滑算法是非常重要的。该研究项目的主要研究者于1987年开发了非高斯滤波器/平滑器，最近又开发了蒙特卡罗滤波器，可以应用于高维一般状态空间模型。在此基础上，提出了一种同时估计状态和参数的方法。在[1]（在研究报告中）中，Kitagawa总结了非线性非高斯状态空间模型的状态和参数估计以及自组织状态空间模型的同步估计的整个发展过程。在b[2]中，Kawasaki等人提出了一种方法，可以缓解观测维数远远高于状态维数时出现的困难。1980年，Higuchi提出了小计数数据的季节调整方法。在[4]中，Kitagawa扩展了自组织滤波器的方法，从创新系列中开发了一种自动均匀识别模型噪声分布的方法。研究中建立的模型和数值计算方法被应用于金融、经济和地球科学等各种问题。研究报告在金融数据波动率估计和GPS数据自动分析方面取得了一些成果。

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.