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

状态空间模型参数估计及其应用研究

基本信息

批准号：
09680318
负责人：
KITAGAWA Genshiro
金额：
$ 1.98万
依托单位：
The Institute of Statistical Mathematics
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09680318/
关键词：
Time Series Analysis State space model Nonlinear Non-Gaussian model Self-organization Monte Carlo filter Smoothing Stochastic Volatility model

项目摘要

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.

在时间序列分析领域，经常使用基于状态空间模型的统一方法。近年来，对于各种重要的真实的世界问题，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器不能给出有效的状态估计，因此发展适用于一般状态空间模型的滤波和平滑算法就显得尤为重要。本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，最近又开发了可应用于高维一般状态空间模型的蒙特卡罗滤波器。在文献[1]（研究报告）中，Kitagawa综述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状态和参数同时估计的整个发展过程。在[2]中，川崎等人提出了一种方法来减轻当观测维数远高于状态维数时所产生的困难。Higuchi在[3]中提出了一种小计数数据的季节调整方法。在[4]中，Kitagawa扩展了自组织滤波方法，发展了一种从新息序列中自动识别模型噪声分布的方法，并将研究中发展的模型和数值计算方法应用于金融、经济和地球科学等各种问题。该研究报告包括金融数据波动性估计和GPS数据自动分析的一些结果。