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Research on Nemerical Methods in Time Series Analysis

Research Project

Project/Area Number 06680295
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Statistical science
Research InstitutionThe Institute of Statistical Mathematics

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)

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)
Project Period (FY) 1994 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1995: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1994: ¥900,000 (Direct Cost: ¥900,000)
KeywordsTime series analysis / State space model / State estimation / Monte Carlo filter / Smoothing / Nonlinear model / Genetic algorithm / Self-organization / 非定常
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.

Report

(3 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] Genshiro Kitagawa: "Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models" Journal of Computational and Graphical Statistics. 5. 1-25 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 北川 源四郎: "モンテカルロ・フィルタおよび平滑化について" 統計数理. 44(印刷中). (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kawano, H.: "The Bootstrap Method in Space Physics : Error Estimation for the Minimum Variance Analysis" Geophysical Research Letter. 22. 307-310 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Higuchi, T.: "Time series analysis of groundwater radon using stochastic differectial equations" Journal of Physics of the Earth. 43. 117-130 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Ohtani,S.: "Magnetic signatures associated with tail current disruption : Fractal analysis" Journal of Geophysical Research. 100. 19135-19145 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 樋口 知之: "遺伝的アルゴリズムとモンテカルロフィルタ" 統計数理(印刷中). 44. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 北川 源四郎: "時系列解析の実際 II" 朝倉書店, 218 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kitagawa, G.: "Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models" Journal of Computational and Graphical Statistics. 5. 1-25 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kitagawa, G.: "On Monte Carlo filter and Smoother (in Japanese with English abstract)" Proceedings of the Institute of Statistical Mathematics. 44 (to appear). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kawano, H.: "The Bootstrap Method in Space Physics : Error Estimation for the Minimum Variance Analysis" Geophysical Research Letter. 22. 307-310 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Higuchi, T.: "Time series analysis of groundwater radon using stochastic differential equations" Journal of Physics of Earth. 43. 117-130 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Ohtani, S.: "Magnetic signatures associated with tail current disruption : Fractal analysis" Journal of Geophysical Research. 100. 19135-19145 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Higuchi, T.: Proceedings of the Institute of Statistical Mathematics. 44 (to apear). (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Kitagawa, G.: Practice of Time Series Analysis (in Japanese). Asakura Publishing Company, 218 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Genshiro Kitagawa: "Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models" Journal of Computational and Graphical Statistics. 5. 1-25 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 北川 源四郎: "モンテカルロ・フィルタおよび平滑化について" 統計数理(印刷中). 44. (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] Kawano,H.: "The Bootstrap Method in Space Physics : Error Estimation for the Minimum Variance Analysis" Geophysical Research Letter. 22. 307-310 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Higuchi,T.: "Time series analysis of groundwater radon using stochastic differential equations" Journal of Physics of the Earth. 43. 117-130 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Ohtani,S.: "Magnetic signatures associated with tail current disruption : Fractal analysis" Journal of Geophysical Research. 100. 19135-19145 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 樋口 知之: "遺伝的アルゴリズムとモンテカルロフィルタ" 統計数理. 44(印刷中). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 北川 源四郎: "時系列解析の実際 II" 朝倉書店, 218 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Kitagawa,Genshiro: "The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother" Annals of the Institute of Statistical Mathematics. Vol.46. 605-623 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 北川源四郎: "マルコフ切り換え自己回帰モデル" 統計数理. 42. 75-82 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Kawano,H.: "The bootstrap method in space physics:Error estimation for the minimum variance analysis" Geophysical Research Letters. 22. 307-310 (1995)

    • Related Report
      1994 Annual Research Report

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Published: 1994-04-01   Modified: 2016-04-21  

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