Relativization of time and a new correlation analysis

• Project/Area Number: 24650148
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Statistical science
• Research Institution: The University of Tokyo
• Principal Investigator: YOSHIDA Nakahiro 東京大学, 数理(科)学研究科(研究院), 教授 (90210707)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 統計数学 / 解析学 / 非同期共分散推定量 / リード・ラグ / 非同期観測 / 共分散

Outline of Final Research Achievements

Statistical properties, implementation and applications of the lead-lag index were investigated. For modeling of market microstructure applicable to the price model and the limit order book, a point process regression model was proposed and limit theorems of the maximum likelihood type estimator for the model were obtained. The lead-lag between two stochastic processes is captured by the coefficients of the Hawkes type intensity functions. A stochastic regression model was presented and it was shown that this model can be a basic model that expresses nonlinear relations at the volatility.

Research Products

• [Journal Article] The YUIMA Project: A Computational Framework for Simulation and Inference of Stochastic Differential Equations (2014)
  • Author(s): A. Brouste, M. Fukasawa, H. Hino, S. M. Iacus, K. Kamatani, Y. Koike, H. Masuda, R. Nomura, T. Ogihara, Y. Shimizu, M. Uchida, N. Yoshida
  • Journal Title: Journal of Statistical Software Volume: 57, no. 4 Pages: 1-51
  • Peer Reviewed
• [Journal Article] Quasilikelihood analysis for nonsynchronously observed diffusion processes (2014)
  • Author(s): T. Ogihara and N. Yoshida
  • Journal Title: Stochastic Processes and their Applications Volume: 124, no.9 Issue: 9 Pages: 2954-3008
  • DOI: 10.1016/j.spa.2014.03.014
  • Peer Reviewed
• [Journal Article] The yuima project: A computational framework for simulation and inference of stochastic differential equations (2014)
  • Author(s): Brouste, A., ,Fukasawa, M., Hino, H., Iacus, S., Kamatani, K., Koike, Y., Masuda, H., Nomura, R., Ogihara, T., Shimuzu, Y., Uchida M., and Yoshida, N.
  • Journal Title: Journal of Statistical Software Volume: 57
  • Peer Reviewed
• [Journal Article] Quasi likelihood analysis of volatility and nondegeneracy of statistical random field (2013)
  • Author(s): Masayuki Uchida and Nakahiro Yoshida
  • Journal Title: Stochastic Processes and their Applications Volume: 123 Issue: 7 Pages: 2851-2876
  • DOI: 10.1016/j.spa.2013.04.008
  • Peer Reviewed
• [Journal Article] Estimation of the lead-lag parameter from non-synchronous data (2013)
  • Author(s): Hoffmann, M., Rosenbaum, M. and Yoshida, N.
  • Journal Title: Bernoulli Volume: 19 Issue: 2 Pages: 363-719
  • DOI: 10.3150/11-bej407
  • Peer Reviewed
• [Presentation] On construction of quasi likelihood analysis for ultra high frequency data (2015)
  • Author(s): Nakahiro Yoshida
  • Organizer: Statistics for Stochastic Processes and Analysis of High Frequency Data IV
  • Place of Presentation: University Pierre and Marie Curie (Paris 6), France
  • Year and Date: 2015-03-23
• [Presentation] Ultra high frequency data and statistical inference : back to the continuous-time paradigm (2015)
  • Author(s): Nakahiro Yoshida
  • Organizer: Statistique Asymptotique des Processus Stochastiques X
  • Place of Presentation: Universite du Maine, France
  • Year and Date: 2015-03-17
  • Invited
• [Presentation] 超高頻度データと統計的漸近理論 (2015)
  • Author(s): 吉田朋広
  • Organizer: 第9回日本統計学会春季集会
  • Place of Presentation: 明治大学（東京都中野区中野）
  • Year and Date: 2015-03-08
• [Presentation] Estimation of point process regression models (2015)
  • Author(s): Nakahiro Yoshida
  • Organizer: 大規模統計モデリングと計算統計
  • Place of Presentation: 東京大学（東京都目黒区駒場）
  • Year and Date: 2015-02-07
• [Presentation] 高頻度データ解析における高次極限定理 (2014)
  • Author(s): 吉田朋広
  • Organizer: 2014年度統計関連学会連合大会
  • Place of Presentation: 東京大学（東京都文京区本郷）
  • Year and Date: 2014-09-16
• [Presentation] Volatility model selection (2014)
  • Author(s): Nakahiro Yoshida
  • Organizer: Dynstoch 2014
  • Place of Presentation: University of Warwick, United Kingdom
  • Year and Date: 2014-09-11
• [Presentation] Statistics of volatility: non-ergodic statistics and stochastic analysis (2014)
  • Author(s): Nakahiro Yoshida
  • Organizer: 11th International Vilnius Conference on Probability Theory and Mathematical Statistics
  • Place of Presentation: Vilnius University, Lithuania
  • Year and Date: 2014-07-02
  • Invited
• [Presentation] YUIMA II: an R package for statistical analysis and simulation for stochastic differential equations (2013)
  • Author(s): Nakahiro Yoshida
  • Organizer: Statistics for Stochastic Processes II: Inference, Limit Theorems, Finance and Data Analysis
  • Place of Presentation: UPMC, Paris
• [Presentation] Estimation of diffusions and limit theorems (2012)
  • Author(s): Nakahiro Yoshida
  • Organizer: 8th World Congress in Probability and Statistics
  • Place of Presentation: Grand Cevahir Hotel and Convention Center, Istanbul
  • Invited
• [Presentation] Asymptotic methods applied to finance and implementation with YUIMA II (2012)
  • Author(s): Nakahiro Yoshida
  • Organizer: DYNSTOCH 2012
  • Place of Presentation: Institut Henri Poincaré, Amphithéatre Perrin, Paris
• [Presentation] Asymptotic expansion methods for stochastic processes and their applications to statistics and finance
  • Author(s): Yoshida, N.
  • Organizer: International Statistical Institute The 59th World Statiscs Congress
  • Place of Presentation: 香港
  • Invited
• [Presentation] Statistics for volatility: change point, model selection, and lead lag
  • Author(s): Yoshida, N.
  • Organizer: 統計数理研究所リスク解析戦略研究センター 第２回金融シンポジウム「ファイナンスリスクのモデリングと制御」
  • Place of Presentation: 東京
• [Presentation] Inferential statistics for volatility under high and ultra high frequent sampling schemes: QLA, model selection, and lead-lag
  • Author(s): Yoshida, N.
  • Organizer: Statistical Analysis and Related Topics: Theory, Methodology, and Data Analysis
  • Place of Presentation: パリ
• [Remarks] 東京大学大学院数理科学研究科 統計グループ
  • URL: http://www2.ms.u-tokyo.ac.jp/probstat/?page_id=15
• [Remarks] 東京大学大学院数理科学研究科 統計グループ
  • URL: http://www2.ms.u-tokyo.ac.jp/probstat/?page_id=15