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Research on Nemerical Methods in Time Series Analysis

时间序列分析中的数值方法研究

基本信息

批准号：
06680295
负责人：
KITAGAWA Genshiro
金额：
$ 0.96万
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 General Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1995
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06680295/
关键词：
Time series analysis State space model State estimation Monte Carlo filter Smoothing Nonlinear model Genetic algorithm Self-organization 非定常

项目摘要

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.

研究了基于非线性非高斯状态空间模型的时间序列分析方法。特别地，针对非线性非高斯状态空间模型的状态估计，提出了蒙特卡罗滤波器和平滑器。作为这项研究的结果，它成为可能的模型高维非线性非高斯系统。我们还开发了一个Monte Carlo后验均值平滑，几乎所有的粒子收敛到边缘后验分布的平均值。这些新方法已成功地应用于经济时间序列的季节调整、卫星数据的准周期运动分析和计数数据的分析等新的统计分析方法的开发中，考虑到蒙特卡罗滤波与遗传算法的相似性，Higuchi提出了一种新的非线性非高斯状态空间模型滤波算法，在研究过程中，为进一步的研究提供了新的思路。在状态空间建模中，采用数值优化方法对模型参数进行估计。该方法需要对系统的似然性进行多次估计，有时会给估计带来很大的困难，考虑到MonteCarlo滤波器可以应用于高维非线性系统，我们在状态向量上增加了未知参数。通过状态向量的这种修改，现在可以同时估计未知状态和模型参数。基于这一思想，我们开发了一个自校正的时间序列模型，它具有自动调整其未知参数的能力。