1995 Fiscal Year Final Research Report Summary
Research on Nemerical Methods in Time Series Analysis
| Project/Area Number |
06680295
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Statistical science
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
KITAGAWA Genshiro The Institute of Statistical Mathematics, Department of Prediction and Control, Professor, 予測制御研究系, 教授 (20000218)
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| Co-Investigator(Kenkyū-buntansha) |
JIANG Xing-qi Asahikawa University, Department of Economics, Associate Professor, 経済学部, 助教授 (70254662)
KAWASAKI Yoshinori The Institute of Statistics Mathematics, Department of Prediction and Control, A, 予測制御研究系, 助手 (70249910)
HIGUCHI Tomoyuki The Institute of Statistics Mathematics, Department of Prediction and Control, A, 予測制御研究系, 助教授 (70202273)
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| Project Period (FY) |
1994 – 1995
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| Keywords | Time series analysis / State space model / State estimation / Monte Carlo filter / Smoothing / Nonlinear model / Genetic algorithm / Self-organization |
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| Research Abstract |
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.
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