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局外母数をもつ時系列回帰モデルのセミパラメトリックな高次漸近理論

Research Project

Project/Area Number 17650081
Research Category

Grant-in-Aid for Exploratory Research

Allocation TypeSingle-year Grants
Research Field Statistical science
Research InstitutionWaseda University

Principal Investigator

谷口 正信  Waseda University, 理工学術院, 教授 (00116625)

Co-Investigator(Kenkyū-buntansha) 鈴木 武  早稲田大学, 理工学術院, 教授 (60047347)
井上 淳  早稲田大学, 政治経済学術院, 教授 (80298174)
蛭川 潤一  早稲田大学, 理工学術院, 助手 (10386617)
玉置 健一郎  早稲田大学, 理工学術院, 助手 (80409664)
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywords時系列解析 / 高次の漸近理論 / 漸近有効性 / セミパラメトリック推定 / 統計的金融工学 / 局所漸近正規性 / 局所定常過程
Research Abstract

セミパラメトリックな高次推定では、時系列回帰モデルにおいて回帰係数の推定に残差スペクトルの非母数的推定量に基づいたHannan推定量の高次のasymptoticsを明らかにした。結果として通常の高次セミパラメトリック推定では、関与の推定量の分布の高次項は非母数推定量のカーネル関数に依存するが、Hannan推定量は、2次までの近似項がカーネル関数に依存しないという結論を得た。これは、従来のこの分野の結果と本質的に異なり、Hannan推定量の特殊性を示している。
非正則モデルの統計解析においては、定常過程のスペクトル密度関数が不連続点を持つ場合のスペクトルのダイナミクス母数と不連続周波点の推測を行った。この結果、不連続周波点の推定量のasymptoticsは従来のそれと異なり、また漸近有効性の面でも、最尤推定量が一般に漸近有効とはならないで、Bayes推定量が漸近有効となることが判明し、従来の推定論と大きく異なることが判明した。
正規過程の共分散関数の推定において、従来は標本共分散を用いるが、標本共分散関数で縮小、拡大項をつけた推定量を提案し、このasymptoticsを明らかにした。従来の標本共分散と新しい推定量は、3次の漸近理論の意味で、差があり、この差を2乗誤差で評価した。自己回帰モデルなどでは、単位根に近いほど、新しい推定量が従来のを改善していることが判明した。
その他、局所定常時系列の判別解析で、理論的結果を得、その応用でも種々の結果を得た。

Report

(3 results)
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (28 results)

All 2008 2007 2006 2005

All Journal Article (17 results) (of which Peer Reviewed: 9 results) Presentation (8 results) Book (3 results)

  • [Journal Article] Asymptotic efficiency of conditional least squares estimators for ARCH models2008

    • Author(s)
      Amano, T.and Taniguchi, M.
    • Journal Title

      Statist.Prob.Letters 78-2

      Pages: 179-185

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Non-regular estimation theory for piecewise continuous spectral densities2008

    • Author(s)
      Taniguchi, M.
    • Journal Title

      Stochastic Processes and Their Applications 118

      Pages: 153-170

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Statistical estimation errors of VaR under ARCH returns2008

    • Author(s)
      Taniai, H.and Taniguchi, M.
    • Journal Title

      J.Statist.Plan.Inference (in press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification and similarity analysis of fundamental frequency patterns iinfant spoken language acquisition2008

    • Author(s)
      Kato, H., Taniguchi, M., Nakatani, T.and Amano, S.
    • Journal Title

      Statistical Methodology (in press)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Statistical estimation of optimal portfolios for non-Gaussian dependent returns of assets2008

    • Author(s)
      Shiraishi, H.and Taniguchi, M.
    • Journal Title

      J.Forecasting (in press)

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Generalized information criteria in model selection for locally stationary processes2008

    • Author(s)
      Hirukawa, J., Kato, H., Tamaki, K.and Taniguchi, M.
    • Journal Title

      J.Jap.Statist.Soc. (in press)

    • NAID

      10030993658

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Bernstein-von Mises theorem for stationary processes2008

    • Author(s)
      Tamaki, K.
    • Journal Title

      J.Jap.Statist.Soc. (in press)

    • NAID

      10030993823

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Improved estimation for the autocovariances of a Gaussian stationary process2007

    • Author(s)
      Taniguchi, M., Shiraishi, H.and Ogata, H.
    • Journal Title

      Statistics 41-4

      Pages: 269-277

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Second order optimality for estimators in time series regression models2007

    • Author(s)
      Tamaki, K.
    • Journal Title

      J.Multivariate Anal. 98

      Pages: 638-659

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Power properties of empirical likelihood for stationary processes2007

    • Author(s)
      Tamaki, K.
    • Journal Title

      Scientiae Mathematicae Japonicae 66-3

      Pages: 359-369

    • NAID

      10019780460

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Higher order asymptotic option valuation for non-Gaussian dependent returns2007

    • Author(s)
      Tamaki, K., Taniguchi, M.
    • Journal Title

      J. Statist. Inference (M.L.Puri Volume) 137

      Pages: 1043-1058

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Second order optimality for estimators in time series regression models2007

    • Author(s)
      Tamaki, K.
    • Journal Title

      J. Multivariate Anal. 98

      Pages: 638-659

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Multiplicatively modulated nonlinear autoregressive model and its applications to biomedical signal analysis2006

    • Author(s)
      Kato.H., Taniguchi.M., Honda.M.
    • Journal Title

      IEEE Trans. Sienal Processing Vol.54-9

      Pages: 3414-3425

    • Related Report
      2006 Annual Research Report
  • [Journal Article] LAN theorem for non-Gaussian locally stationary processes and its applications2006

    • Author(s)
      Hirukawa, J., Taniguchi, M.
    • Journal Title

      J. Statist. Plan. Inference 136-3

      Pages: 640-688

    • Related Report
      2006 Annual Research Report
  • [Journal Article] LAN theorem for non-Gaussian locally stationary processes and its applications2006

    • Author(s)
      Hirukawa, J., Taniguchi, M.
    • Journal Title

      J.Statist.Plan.Inf. 136

      Pages: 640-688

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Minimum alpha-divergence estimation for ARCH models2006

    • Author(s)
      Chandra, A., Taniguchi, M.
    • Journal Title

      J.Time Ser.Anal. 27, 1

      Pages: 19-39

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The Stein-James estimator for short- and long-memory Gaussian processes2005

    • Author(s)
      Taniguchi, M., Hirukawa, J.
    • Journal Title

      Biometrika 92, 3

      Pages: 737-746

    • Related Report
      2005 Annual Research Report
  • [Presentation] Generalized information criteria in model selection for locally stationary processes2008

    • Author(s)
      蛭川 潤一、玉置 健一郎、加藤 比呂子、谷口 正信
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] Preliminary test estimation for spectra and its applications to financial hedging problem2008

    • Author(s)
      前山 裕亮、玉置 健一郎、谷口 正信
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] Statistical testing for asymptotic no-arbitrage in financial markets2008

    • Author(s)
      畑井 一平、白石 博、谷口 正信
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] 時系列モデルに対する高次漸近理論2008

    • Author(s)
      玉置 健一郎
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] On adjustment based on the signed root empirical likelihood for linear regression model2007

    • Author(s)
      玉置 健一郎
    • Organizer
      日本数学会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Power properties of empirical likelihood for stationary processes2007

    • Author(s)
      玉置 健一郎
    • Organizer
      日本数学会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Systematic approach for portmanteau tests in view of Whittle likelihhod ratio2007

    • Author(s)
      谷口 正信、天野 友之
    • Organizer
      日本数学会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Asymptotic inference for locally stationary processes2007

    • Author(s)
      蛭川 潤一
    • Organizer
      日本数学会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Book] Optimal Statistical lnference in Financial Engineering2008

    • Author(s)
      Taniguchi, M., Hirukawa, J.and Tamaki, K.
    • Total Pages
      384
    • Publisher
      Chapman & Hall/CRC
    • Related Report
      2007 Annual Research Report
  • [Book] Optimal Statistical Inference in Financial Engineering2007

    • Author(s)
      Taniguchi, M., Hirukawa, J., Tamaki, K.
    • Total Pages
      400
    • Publisher
      Chapman-Hall(in press)
    • Related Report
      2006 Annual Research Report
  • [Book] 数理統計・時系列・金融工学2005

    • Author(s)
      谷口 正信
    • Total Pages
      211
    • Publisher
      朝倉書店
    • Related Report
      2005 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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