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Statistical mechanical study of stochastic models for time correlation in stock markets

Research Project

Project/Area Number 15K01190
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Social systems engineering/Safety system
Research InstitutionOkayama University

Principal Investigator

Murai Joshin  岡山大学, 社会文化科学研究科, 教授 (00294447)

Research Collaborator Kuroda Koji  
Maskawa Jun-ichi  
Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywordsクラスター展開 / ハースト指数 / 取引符号 / 長期記憶 / 非整数ブラウン運動 / バースト現象 / Hurst指数
Outline of Final Research Achievements

By analyzing huge high frequency data in stock market, phenomena that can not be observed in daily data are discovered one after another. In this study, we have theoretically studied the causes of long-term memory of the transaction signs among those phenomena, using statistical mechanics methods. Based on the hypothesis that the origin is in the divided orders of potential orders by individual investors, we define a discrete time stochastic process that represents the cumulative transaction signs, and use the method of the cluster expansion of statistical mechanics to obtain a continuous time stochastic processes as its scale limit. It is shown that the time stochastic process is the superposition of Brownian motion and multiple fractional Brownian motions with different Hurst exponents.

Academic Significance and Societal Importance of the Research Achievements

累積取引符号を表す離散型確率過程のスケール極限の連続時間確率過程がブラウン運動と異なるハースト指数を持つ複数の非整数ブラウン運動の重ね合わせになることを示したが,これらのハースト指数は1/2以上,すなわち得られた確率過程の増分は長期記憶を持つことが示された。先行研究では,取引頻度の高い投資家の投資行動が取引符号の長期記憶を生み出す主な原因と考えられていたが,本研究で構成された連続時間確率過程のハースト指数に最大の寄与をするのは,取引頻度が中間的な投資家であるという興味深い結果が得られた。

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (12 results)

All 2018 2017 2016 2015

All Journal Article (4 results) (of which Peer Reviewed: 3 results,  Acknowledgement Compliant: 1 results,  Open Access: 1 results) Presentation (8 results) (of which Int'l Joint Research: 3 results,  Invited: 1 results)

  • [Journal Article] Multiplicative random cascades with additional stochastic process in financial markets2018

    • Author(s)
      Maskawa, J., Kuroda, K. & Murai
    • Journal Title

      J. Evolut Inst Econ Rev

      Volume: 15 Issue: 2 Pages: 515-529

    • DOI

      10.1007/s40844-018-0112-y

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A model of transaction signs with order splitting and public information2016

    • Author(s)
      J.Murai
    • Journal Title

      Evolutionary and Institutional Economics Review

      Volume: 13(2) Issue: 2 Pages: 469-480

    • DOI

      10.1007/s40844-016-0050-5

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Signs of market orders and human dynamics2015

    • Author(s)
      J.Murai
    • Journal Title

      Proceedings of the International Conference on Social Modeling and Simulation, plus Econophysics Colloquium 2014

      Volume: 1 Pages: 39-50

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] 取引間隔の多様なベキ指数と取引符号のハースト指数2015

    • Author(s)
      村井浄信
    • Journal Title

      統計数理研究所共同研究リポート

      Volume: 332 Pages: 97-102

    • Related Report
      2015 Research-status Report
  • [Presentation] Empirical study on random cascades among different time horizons in stock markets2017

    • Author(s)
      Jun-ichi Maskawa, Koji Kuroda, Joshin Murai
    • Organizer
      13th Econophysics Colloquium 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 株式市場におけるマルチフラクタル性のランダム・カスケードモデルによる実証研究2017

    • Author(s)
      増川純一,黒田耕嗣,村井浄信
    • Organizer
      経済物理学 2017 - 新たな領域との融合
    • Related Report
      2017 Research-status Report
  • [Presentation] 注文分割と公開情報による取引符号モデル2016

    • Author(s)
      村井 浄信
    • Organizer
      経済物理とその周辺
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2016-01-09
    • Related Report
      2015 Research-status Report
  • [Presentation] 公開情報への反応関数をもつポリマーモデルにおけるトレンド項2015

    • Author(s)
      村井 浄信
    • Organizer
      無限粒子系、確率場の諸問題XI
    • Place of Presentation
      奈良女子大学理学部
    • Year and Date
      2015-12-26
    • Related Report
      2015 Research-status Report
  • [Presentation] 注文分割と公開情報による取引符号モデル2015

    • Author(s)
      村井 浄信
    • Organizer
      経済物理学 2015: 新たな方向性を求めて
    • Place of Presentation
      京都大学 基礎物理学研究所
    • Year and Date
      2015-12-03
    • Related Report
      2015 Research-status Report
  • [Presentation] A model of order signs under multiple order splitting and public information2015

    • Author(s)
      J.Murai
    • Organizer
      ECONOPHYS-2015
    • Place of Presentation
      New Delhi, India
    • Year and Date
      2015-11-30
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 公開情報と取引符号2015

    • Author(s)
      村井 浄信
    • Organizer
      経済物理とその周辺
    • Place of Presentation
      鳥取大学工学部
    • Year and Date
      2015-09-24
    • Related Report
      2015 Research-status Report
  • [Presentation] Order signs model with order splitting and exogenous herding2015

    • Author(s)
      J.Murai
    • Organizer
      International Conference on Big data in Economics, Science and Technology
    • Place of Presentation
      Ohrid, Republic of Macedonia
    • Year and Date
      2015-07-22
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research

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Published: 2015-04-16   Modified: 2020-03-30  

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