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

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K01190
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Social systems engineering/Safety system
• Research Institution: Okayama 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
• 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

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.

Free Research Field

確率モデル論，経済物理学

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。