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Research on Statistical Theory and Time Series Analysis for Mathematical Finance

Research Project

Project/Area Number 14203003
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Economic statistics
Research InstitutionHitotsubashi University

Principal Investigator

YAMAMOTO Taku  Hitotsubashi University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (50104716)

Co-Investigator(Kenkyū-buntansha) HAYAKAWA Takeshi  Fuji University, Graduate School of Economics and Management System, Professor, 大学院・経済・経営システム研究科, 教授 (00000183)
TAKAHASHI Hajime  Hitotsubashi University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (70154838)
SHIBA Tsunemasa  Hitotsubashi University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (90187386)
TANAKA Katsuto  Hitotsubashi University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (40126595)
KUWANA Yoichi  Hitotsubashi University, Graduate School of Economics, Associate Professor, 大学院・経済学研究科, 助教授 (30272769)
黒住 英司  一橋大学, 大学院・経済学研究科, 助教授 (00332643)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥41,990,000 (Direct Cost: ¥32,300,000、Indirect Cost: ¥9,690,000)
Fiscal Year 2004: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Fiscal Year 2003: ¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2002: ¥21,970,000 (Direct Cost: ¥16,900,000、Indirect Cost: ¥5,070,000)
KeywordsTime series analysis / Statistical theory / Finance / Mathematical finance / Structural change / Wavelet / Financial series / Simulation / 共和分 / 非定常VARモデル / MCMC手法 / 信用スプレッド / バリュー・アット・リスク / デリバティブ / Wald検定 / 裁定価格理論 / バリアー・オプション / 権利行使価格 / 漸近展開 / 長期因果性 / ワルド検定
Research Abstract

1.For analysis of financial and economic time series, the tests for the short-run and the long-run causalities were developed for cointegrated systems.
2.The forecasting procedure for large cointegrated systems was developed. It was made possible by extracting principal components of a large cointegrated system. The experiments and the actual forecasts of stock prices of 25 companies supported its validity.
3.For analysis of economic time series including financial series, the Lagrange Multiplier test was developed for a change in long-run persistence. Statistical properties of the test were investigated. The strength of persistence in Yen/Dollar exchange rate was examined.
4.The new concept, the embedded complete market, was proposed in place of the traditional but restrictive "complete market." Based upon it, a new method for calculating the option price was derived.
5.The pricing of the weather derivative was investigated. Specifically, the model for temperature was developed based upon data of Tokyo and Nagoya in order to derive the weather derivative.
6.Two simulation methods were investigated for econometric model analysis : One was the Beyesian Markov Chain Monte Carlo(MCMC) method, and the other one was non-Bayes bootstrap method.
7.Using the high frequency exchange rate data, the announcement effect of economic indicators was analyzed. Further, the analysis was extended for decomposed baseline data and surprise data.
8.Derivation of the distribution for quadratic functionals of fractional Brownian motion was examined. While the exact results were unsolved, some conjectures were given. The prediction on a simple result for moments was obtained.
9.After investigating the traditional time-domain and frequency-domain approaches for parameter estimation in non-stationary or long memory time series, they were compared with the wavelet-based estimators. It was found that the wavelet-based method gives more accurate results than the traditional ones.

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (52 results)

All 2005 2004 2003 2002 Other

All Journal Article (28 results) Book (2 results) Publications (22 results)

  • [Journal Article] Equivalence of Two Expressions of the Impact Matrix2005

    • Author(s)
      黒住英司, 千木良弘朗, 山本拓
    • Journal Title

      Econometric Theory (印刷中)

    • NAID

      120000823627

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Embedded Complete Markets2005

    • Author(s)
      高橋一
    • Journal Title

      Hitotsubashi Journal of Economics 46-1

      Pages: 99-110

    • NAID

      110007629878

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] ウェーブレット解析の統計学への応用について2005

    • Author(s)
      田中勝人
    • Journal Title

      数学 57

      Pages: 50-69

    • NAID

      10016419132

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Equivalence of Two Expressions of the Impact Matrix2005

    • Author(s)
      Eiji Kurozumi, Hiroaki Chigira, Taku Yamamoto
    • Journal Title

      Econometric Theory (forthcoming)

    • NAID

      120000823627

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Embedded Complete Markets2005

    • Author(s)
      Hajime Takahashi
    • Journal Title

      Hitotsubashi Journal of Economics 46-1

      Pages: 99-110

    • NAID

      110007629878

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Applications of Wavelet in Statistics(in Japanese)2005

    • Author(s)
      Katsuto Tanaka
    • Journal Title

      Sugaku 57

      Pages: 50-69

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Equivalence of Two Expressions of the Impact Matrix2005

    • Author(s)
      山本 拓
    • Journal Title

      Econometric Theory Vol.21(forthcoming)

    • NAID

      120000823627

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On Embedded Complete Markets2005

    • Author(s)
      高橋 一
    • Journal Title

      Hitotsubashi Journal of Economics 46.1(forthcoming)

    • NAID

      110007629878

    • Related Report
      2004 Annual Research Report
  • [Journal Article] ウェーブレット解析の統計学への応用について2005

    • Author(s)
      田中 勝人
    • Journal Title

      数学(日本数学会) 57・1

      Pages: 50-69

    • NAID

      10016419132

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Frequency Domain and Wavelet-based Estimation for Long Memory Signal Plues Noise Models2004

    • Author(s)
      田中勝人
    • Journal Title

      Festschrift for Professor Durbin(Cambridge University Press)

      Pages: 75-91

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Frequency Domain and Wavelet-based Estimation for Long Memory Signal Plus Noise Models2004

    • Author(s)
      Katsuto Tanaka
    • Journal Title

      Festschrift for Professor Durbin(Cambridge University Press)

      Pages: 75-91

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Frequency Domain and Wavelet-based Estimation for Long-memory Signal plus Noise Models2004

    • Author(s)
      田中 勝人
    • Journal Title

      Festschrift for Professor Durbin (Cambridge University Press)

      Pages: 75-91

    • Related Report
      2004 Annual Research Report
  • [Journal Article] ある種の統計量の事後分布の漸近分布の漸近展開について2003

    • Author(s)
      早川毅
    • Journal Title

      京都大学数理解析研究所講究録「漸近的統計理論」 1308

      Pages: 20-28

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Finite Sample Properties of the Granger Non-Causality Test in Possibly Cointegrated Systems2003

    • Author(s)
      山本拓, 千木良弘朗
    • Journal Title

      Bulletin of the International statistical Institute 60

      Pages: 666-667

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Asymptotic Expansion of Asymptotic Distribution of Posterior Distribution of a Certain Statistic(in Japanese)2003

    • Author(s)
      Takeshi Hayakawa
    • Journal Title

      Research Institute of Mathematical Sciences, Kyoto University, Research Memorandum in Asymptotic Statistical Theory 1308

      Pages: 20-28

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Finite Sample Properties of the Granger Non-Causality Test in Possibly Cointegrated Systems2003

    • Author(s)
      Taku Yamamoto, Hiroaki Chigira
    • Journal Title

      Bulletin of the International Statistical Institute 60

      Pages: 666-667

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Independence of Likelihood Ratio Criterion for Homogeniety of Several Populations2002

    • Author(s)
      早川毅
    • Journal Title

      Annals of the Institute of Statistical Mathematics 54

      Pages: 918-933

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Testing for Stationarity with a Break2002

    • Author(s)
      黒住英司
    • Journal Title

      Journal of Econometrics 108

      Pages: 63-99

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Testing for Periodic Stationarity2002

    • Author(s)
      黒住英司
    • Journal Title

      Econometric Reviews 21

      Pages: 243-270

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] The Limiting Properties of the Canova-Hansen Test under Alternatives2002

    • Author(s)
      黒住英司
    • Journal Title

      Econometric Theory 18

      Pages: 1197-1220

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Pricing Exponential Square Root Barrier Knockout European Options2002

    • Author(s)
      森本真由美, 高橋一
    • Journal Title

      Asia-Pacific Financial Markets 9

      Pages: 1-21

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A Unified Approach to the Measurement Error Problem in Time Series Models2002

    • Author(s)
      田中勝人
    • Journal Title

      Econometric Theory 18

      Pages: 278-296

    • NAID

      120006933868

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Independence of Likelihood Ratio Criterion of Homogeniety of Several Populations2002

    • Author(s)
      Takeshi Hayakawa
    • Journal Title

      Annals of the Institute of Statistical Mathematics 54

      Pages: 918-933

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Testing for Stationarity with a Break2002

    • Author(s)
      Eiji Kurozumi
    • Journal Title

      Journal of Econometrics, 108

      Pages: 63-99

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Testing for Periodic Stationarity2002

    • Author(s)
      Eiji Kurozumi
    • Journal Title

      Econometric Reviews 21

      Pages: 243-270

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] The Limiting Properties of the Canova-Hansen Test Under Alternatives2002

    • Author(s)
      Eiji Kurozumi
    • Journal Title

      Econometric Theory 18

      Pages: 1197-1220

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On Pricing Exponential Square Root Barrier Knockout European Options2002

    • Author(s)
      Mayumi Morimoto, Hajime Takahashi
    • Journal Title

      Asia-Pacific Financial Markets 9

      Pages: 1-21

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A Unified Approach to the Measurement Error Problem in Time Series Models2002

    • Author(s)
      Katsuto Tanaka
    • Journal Title

      Econometric Theory 18

      Pages: 278-296

    • NAID

      120006933868

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] 経済時系列の統計-その数理的基礎2003

    • Author(s)
      刈屋武昭, 田中勝人, 矢島美寛
    • Total Pages
      318
    • Publisher
      岩波書店
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] Statistics for Economic Time Series : Mathmatical Foundations.(in Japanese)2003

    • Author(s)
      Takeaki Kariya, Katsuto Tanaka, Yoshihiro Yajima
    • Total Pages
      318
    • Publisher
      Iwanami Shoten
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] 田中勝人: "計量経済学のテキストを書き換えた「共和分」と「単位根」概念"経済セミナー. 588号. 73-76 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 田中勝人: "ウェーブレット解析の統計学への応用について"数学. (未定). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 田中勝人: "Frequency domain and wavelet-based estimation for long-memory signal plus noise models"Festschrift for Professor Durbin(Cambridge University Press). 75-91 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 早川毅: "ある種の統計量の事後分布の漸近展開について"数理解析研究所講究録. 1308号. 20-28 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 山本拓, 黒住英司: "Tests for Long-Run Granger Non-Causality in Cointegrated Systems"Discussion Paper #2003-12, Graduate School of Economics, Hitotsubashi University, June 2003. #12. 1-39 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 黒住英司: "Some Properties of the Point Optimal Invariant Test for the Constancy of Parameters"Journal of the Japan Statistical Society. Vol.33,No.2. 169-180 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 千木良 弘明, 山本拓: "The Granger Non-Causality Test in Cointegrated Vector Autoregressions"Discussion Paper #2003-13, Graduate School of EconoMics, totsubashi University, June 2003. #13. 1-28 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 斯波 恒正: "APT with Time Varying and Fixed Risk Premia : an MCMC approach"SepteMber, 2003, mimeo, 7 pages. 1-7 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 斯波 恒正: "Metropolis-Hastings Sampler : A Simple Regression Example"September, 2003, mimeo, 14 pages. 1-14 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 高橋一, 元山斉: "On Normal Approximation for the Statistical Functionals in Finite Population"Dec. 2003 Manuscript. 1-8 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 黒住英司: "穴埋め式 統計数理らくらくワークブック(藤田岳彦監修)"講談社. 168 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 早川 毅: "Independence of Likelihood Ratio Criteria for Homogeneity of Several Populations"Annals of the Institute of Statistical Mathematics. Vol.54,No.. 918-933 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 高橋 一: "On Pricing Exponential Square Root Barrier Knockout European Options, "Asia-Pacific Financial Market, Vol.9,2002(with Morimoto),PP.1-21"Asia-Pacific Financial Market. Vol.9. 1-21 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 斯波 恒正: "ファイナンスにおける時系列手法--単位根を持つ時系列"証券アナリスト・ジャーナル. 第40巻4号. 97-114 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 斯波 恒正: "ファイナンスにおける時系列手法--非線形時系列のモデル"証券アナリスト・ジャーナル. 第40巻7号. 58-72 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 斯波 恒正: "ファイナンスにおける時系列手法--季節性分解法"証券アナリスト・ジャーナル. 第40巻10号. 83-104 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 田中 勝人: "A Unified Approach to the Measurement Error Problem in Time Series Models"Econometric Theory. Vol.18,No.2. 278-296 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 黒住 英司: "Testing for Stationarity with a Break"Journal of Econometrics. Vol.108. 63-99 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 黒住 英司: "The Limiting Properties of the Canova-Hansen Test Under Local Alternatives"Econometric Theory. Vol.18,No.6. 1197-1220 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 黒住 英司: "Testing for Periodic Stationarity"Econometric Reviews. Vol.21,No.2. 243-270 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 田中 勝人: "経済統計(第2版)"岩波書店. 228 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 刈屋 武昭, 田中 勝人 他: "経済時系列の統計-その数理的基礎"岩波書店. 318 (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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