• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Theoretical statistics for stochastic processes and limit theorems

Research Project

Project/Area Number 24340015
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionThe University of Tokyo

Principal Investigator

Yoshida Nakahiro  東京大学, 数理(科)学研究科(研究院), 教授 (90210707)

Co-Investigator(Kenkyū-buntansha) MASUDA Hiroki  九州大学, 大学院数理学研究院, 教授 (10380669)
Co-Investigator(Renkei-kenkyūsha) MURATA Noboru  早稲田大学, 理工学術院, 教授 (60242038)
UCHIDA Masayuki  大阪大学, 大学院基礎工学研究科, 教授 (70280526)
SHIMIZU Yasutaka  早稲田大学, 理工学術院, 准教授 (70423085)
FUKASAWA Masaaki  大阪大学, 大学院基礎工学研究科, 教授 (70506451)
KAMATANI Kengo  大阪大学, 大学院基礎工学研究科, 講師 (00569767)
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥18,070,000 (Direct Cost: ¥13,900,000、Indirect Cost: ¥4,170,000)
Fiscal Year 2014: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2013: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2012: ¥6,760,000 (Direct Cost: ¥5,200,000、Indirect Cost: ¥1,560,000)
Keywords漸近展開 / Malliavin解析 / 極限定理 / 確率過程の統計学 / 擬似尤度解析 / 非同期共分散推定 / ボラティリティ / セミマルチンゲール / 統計数学 / 機械学習 / 解析学 / 確率論 / 確率過程 / 漸近理論 / ファイナンス / マルチンゲール展開 / 疑似尤度解析
Outline of Final Research Achievements

The quasi likelihood analysis was constructed for a stochastic regression model of volatility based on high frequency data in the finite time horizon, and an analytic criterion and a geometric criterion for non-degeneracy of the statistical random field associated with the quasi likelihood function were provided. The asymptotic mixed normality and the convergence of moments were proved. A quasi likelihood analysis was developed for a non-synchronously observed stochastic differential equation. Asymptotic expansion for a martingale with mixed normal limit was established. It is a new limit theorem beyond the frame of the present theory of asymptotic expansion for ergodic processes. The martingale expansion was applied to the p-variation. Studies of the asymptotic expansion of volatility estimators under microstructure noise have been developed. The spot volatility information criterion sVIC was proposed, and the fundamentals for developing computer software were studied.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (53 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (8 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 8 results) Presentation (38 results) (of which Int'l Joint Research: 12 results,  Invited: 11 results) Book (1 results) Remarks (3 results) Funded Workshop (3 results)

  • [Journal Article] Edgeworth expansion for functionals of continuous diffusion processes2016

    • Author(s)
      Podolskij, M. and Yoshida. N.
    • Journal Title

      Annals of Applied Probability

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Model selection for volatility prediction2015

    • Author(s)
      Uchida, M. and Yoshida, N.
    • Journal Title

      The Fascination of Probability, Statistics and their Applications. In Honour of Ole E. Barndorff-Nielsen

      Volume: 0 Pages: 343-360

    • DOI

      10.1007/978-3-319-25826-3_16

    • ISBN
      9783319258249, 9783319258263
    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The yuima project: A computational framework for simulation and inference of stochastic differential equations2014

    • 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

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Edgeworth expansion for the integrated Levy driven Ornstein-Uhlenbeck process2013

    • Author(s)
      H. Masuda and N. Yoshida
    • Journal Title

      Electronic Communications in Probability

      Volume: 18 Issue: none Pages: 1-10

    • DOI

      10.1214/ecp.v18-2726

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quasi likelihood analysis of volatility and nondegeneracy of statistical random field2013

    • 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

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Estimation of the lead-lag parameter from non-synchronous data2013

    • Author(s)
      Hoffmann, M., Rosenbaum, M. and Yoshida, N.
    • Journal Title

      Bernoulli

      Volume: 19 Issue: 2 Pages: 363-719

    • DOI

      10.3150/11-bej407

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Martingale expansion in mixed normal limit2013

    • Author(s)
      N. Yoshida
    • Journal Title

      Stochastic Processes and their Applications

      Volume: 123 Pages: 887-933

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Adaptive estimation of an ergodic diffusion process based on sampled data2012

    • Author(s)
      M. Uchida and N. Yoshida
    • Journal Title

      Stochastic Processes and their Applications

      Volume: 122 Pages: 2885-2924

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] Martingale expansion: its applications and generalizations2016

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      Statistics for Stochastic Processes and Analysis of High Frequency Data V
    • Place of Presentation
      University Pierre and Marie Curie (Paris 6)
    • Year and Date
      2016-03-23
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Asymptotic expansion of quasi likelihood estimators and model selection for volatility2016

    • Author(s)
      吉田朋広
    • Organizer
      ASC2016: Asymptotic Statistics and Computations
    • Place of Presentation
      東京大学(駒場キャンパス)
    • Year and Date
      2016-02-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] Quasi likelihood analysis for ultra high frequency data2015

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      9th Conference of the Asian Regional Section of the IASC (IASC-ARS 2015)
    • Place of Presentation
      National University of Singapore
    • Year and Date
      2015-12-19
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Quasi likelihood analysis for ultra high frequency data2015

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      8th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2015)
    • Place of Presentation
      Senate House, University of London
    • Year and Date
      2015-12-13
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Ultra high frequency data: construction of quasi likelihood analysis, and some data analysis2015

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      Berlin Meeting on Statistical Analysis of Stochastic Processes
    • Place of Presentation
      Humboldt University
    • Year and Date
      2015-11-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Point processes and ultra high frequency data: limit order book modeling2015

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      大規模統計モデリングと計算統計 II
    • Place of Presentation
      東京大学(駒場キャンパス)
    • Year and Date
      2015-09-26
    • Related Report
      2015 Annual Research Report
  • [Presentation] 点過程の推測理論と超高頻度データのモデリング2015

    • Author(s)
      吉田朋広
    • Organizer
      2015年度 統計関連学会連合大会
    • Place of Presentation
      岡山大学(津島キャンパス)
    • Year and Date
      2015-09-07
    • Related Report
      2015 Annual Research Report
  • [Presentation] Asymptotic statistics and ultra hight frequency data2015

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      Advanced Modelling in Mathematical Finance: A conference in honour of Ernst Eberlein
    • Place of Presentation
      University of Kiel
    • Year and Date
      2015-05-22
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On construction of quasi likelihood analysis for ultra high frequency data2015

    • 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
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Ultra high frequency data and statistical inference : back to the continuous-time paradigm2015

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      Statistique Asymptotique des Processus Stochastiques X
    • Place of Presentation
      Universite du Maine, France
    • Year and Date
      2015-03-17
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / 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
      明治大学中野キャンパス
    • Year and Date
      2015-03-08
    • Related Report
      2014 Annual Research Report
  • [Presentation] Estimation of point process regression models2015

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      大規模統計モデリングと計算統計
    • Place of Presentation
      University of Tokyo
    • Year and Date
      2015-02-07
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Asymptotic expansion of functionals of high frequency data and their applications2014

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      7th International Conference of the ERCIM WG on Computational and Methodological Statistics (ERCIM 2014)
    • Place of Presentation
      Senate House, University of London
    • Year and Date
      2014-12-08
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Information criterion sVIC for volatility model selection2014

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      NUS-UTOKYO WORKSHOP ON QUANTITATIVE FINANCE
    • Place of Presentation
      University of Tokyo
    • Year and Date
      2014-09-26
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [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(本郷キャンパス)
    • Year and Date
      2014-09-16
    • Related Report
      2014 Annual Research Report
  • [Presentation] Volatility model selection2014

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      Dynstoch 2014
    • Place of Presentation
      the University of Warwick, United Kingdom
    • Year and Date
      2014-09-11
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Statistics of volatility: non-ergodic statistics and stochastic analysis2014

    • Author(s)
      Nakahiro Yoshida
    • Organizer
      11th International Vilnius Conference on Probability Theory and Mathematical Statistics
    • Place of Presentation
      Vilnius University, Vilnius, Lithuania
    • Year and Date
      2014-07-02
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] ミキシング確率ボラティリティの構造推定と高次極限定理2013

    • Author(s)
      吉田朋広
    • Organizer
      SC2013 Asymptotic Statistics and Computations (主催)
    • Place of Presentation
      東京大学
    • Year and Date
      2013-03-27
    • Related Report
      2012 Annual Research Report
  • [Presentation] YUIMA II : an R package for statistical analysis and simulation for stochastic differential equations2013

    • Author(s)
      吉田朋広
    • Organizer
      Statistics for Stochas-tic Processes II : Inference Limit Theo-rems Finance and Data
    • Place of Presentation
      UPMC (パリ)
    • Year and Date
      2013-03-19
    • Related Report
      2012 Annual Research Report
  • [Presentation] Martingale expansion and applications to realized volatility and power variation2012

    • Author(s)
      吉田朋広
    • Organizer
      SART2012 Statistical Analysis and Related Topics : Theory Methodology and Data Analysis (幸催)
    • Place of Presentation
      東京大学
    • Year and Date
      2012-12-20
    • Related Report
      2012 Annual Research Report
  • [Presentation] Limit theorems in statistics for volatility2012

    • Author(s)
      吉田朋広
    • Organizer
      AMS Sectional Meeting
    • Place of Presentation
      niversity of Arizona (ツーソン)(招待講演)
    • Year and Date
      2012-10-28
    • Related Report
      2012 Annual Research Report
  • [Presentation] ファイナンス統計学における漸近的方法とその実装2012

    • Author(s)
      吉田朋広
    • Organizer
      2012年度統計関連学会連合大会
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-09-11
    • Related Report
      2012 Annual Research Report
  • [Presentation] 確率過程の疑似尤度解析2012

    • Author(s)
      吉田朋広
    • Organizer
      2012年度統計関連学会連合大会
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-09-10
    • Related Report
      2012 Annual Research Report
  • [Presentation] Estimation of diffusions and limit theorems2012

    • Author(s)
      吉田朋広
    • Organizer
      8th World Congress in Probability and Statistics
    • Place of Presentation
      Grand Cevahir Hotel and Convention Center (イスタンブール)(招待講演)
    • Year and Date
      2012-07-13
    • Related Report
      2012 Annual Research Report
  • [Presentation] Limit theorems and estimation for diffusions2012

    • Author(s)
      吉田朋広
    • Organizer
      The 2nd Institute of Mathematical Statistics Asia Pacific Rim Meeting
    • Place of Presentation
      エポカルつくば(招待講演)
    • Year and Date
      2012-07-04
    • Related Report
      2012 Annual Research Report
  • [Presentation] Asymptotic methods applied to finance and implementation with YUIMA II2012

    • Author(s)
      吉田朋広
    • Organizer
      DYNSTOCH 2012
    • Place of Presentation
      Institut Henri Poincare, Amphitheatre Perrin (パリ)
    • Year and Date
      2012-06-08
    • Related Report
      2012 Annual Research Report
  • [Presentation] Nondegeneracy of statistical random field and statistics for stochastic processes2012

    • Author(s)
      吉田朋広
    • Organizer
      S.A.P.S. IX(Statistique Asymptotiques des Processus Stochastiques IX
    • Place of Presentation
      Universite du Maine (ルマン)(招待講演)
    • Year and Date
      2012-03-11
    • Related Report
      2012 Annual Research Report
  • [Presentation] Martingale expansion and statistics of volatility

    • Author(s)
      Yoshida, N.
    • Organizer
      DYNSTOCH WORKSHOP 2013
    • Place of Presentation
      コペンハーゲン
    • Related Report
      2013 Annual Research Report
  • [Presentation] Statistics for Stochastic Differential Equations and Asymptotic Methods

    • Author(s)
      Yoshida, N.
    • Organizer
      ARS CONJECTANDI ( A celebration of 300 years of stochastics)
    • Place of Presentation
      フライブルグ、バーゼル
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Asymptotic statistics for stochastic processes and computational methods

    • Author(s)
      Yoshida, N.
    • Organizer
      29th European Meeting of Statisticians
    • Place of Presentation
      ブタペスト
    • Related Report
      2013 Annual Research Report
    • Invited
  • [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
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] ボラティリティ推定に対する疑似尤度解析の構成について

    • Author(s)
      吉田朋広
    • Organizer
      2013年度 統計関連学会連合大会
    • Place of Presentation
      大阪
    • Related Report
      2013 Annual Research Report
  • [Presentation] 機械学習による漸近展開の近似精度の予測

    • Author(s)
      Hino, H., Nomura, R., Murata, N., Yoshida, N.
    • Organizer
      2013年度 統計関連学会連合大会
    • Place of Presentation
      大阪
    • Related Report
      2013 Annual Research Report
  • [Presentation] Statistics for volatility: change point, model selection, and lead lag

    • Author(s)
      吉田朋広
    • 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
    • Related Report
      2013 Annual Research Report
  • [Presentation] Inference for volatility: Some theoretical aspects

    • Author(s)
      Yoshida, N.
    • Organizer
      6th International Conference of the ERCIM WG on Computational and Methodological Statistics (ERCIM 2013)
    • Place of Presentation
      ロンドン
    • Related Report
      2013 Annual Research Report
    • Invited
  • [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
    • Related Report
      2013 Annual Research Report
  • [Presentation] ボラティリティモデル選択のための情報量規準の構成

    • Author(s)
      Yoshida, N.
    • Organizer
      第三回数理ファイナンス合宿型セミナー
    • Place of Presentation
      静岡
    • Related Report
      2013 Annual Research Report
  • [Presentation] On construction of a volatility information criterion

    • Author(s)
      Yoshida, N.
    • Organizer
      ASC2014 Asymptotic Statistics and Computations
    • Place of Presentation
      東京
    • Related Report
      2013 Annual Research Report
  • [Book] Market Microstructure (の第4章)2012

    • Author(s)
      F. Abergel, J-P Bouchaud, T. Foucault.
    • Publisher
      Wiley
    • Related Report
      2012 Annual Research Report
  • [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/

    • Related Report
      2015 Annual Research Report 2014 Annual Research Report
  • [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

    • Related Report
      2013 Annual Research Report
  • [Remarks]

    • URL

      http://www2.ms.u-tokyo.ac.jp/probstat/?page_id=15

    • Related Report
      2012 Annual Research Report
  • [Funded Workshop] Statistics for Stochastic Processes and Analysis of High Frequency Data V2016

    • Place of Presentation
      University Pierre and Marie Curie (Paris 6), France
    • Year and Date
      2016-03-23
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] Berlin Meeting on Statistical Analysis of Stochastic Processes2015

    • Place of Presentation
      Humboldt Graduate School
    • Year and Date
      2015-11-05
    • Related Report
      2015 Annual Research Report
  • [Funded Workshop] Statistics for Stochastic Processes and Analysis of High Frequency Data IV2015

    • Place of Presentation
      University Pierre and Marie Curie (Paris 6), France
    • Year and Date
      2015-03-23
    • Related Report
      2014 Annual Research Report

URL: 

Published: 2012-04-24   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi