Developing statistical asymptotic theory for jump processes and its applications

• Project/Area Number: 23740082
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyushu University
• Principal Investigator: MASUDA Hiroki 九州大学, マス・フォア・インダストリ研究所, 准教授 (10380669)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 統計的漸近推測 / ジャンプ過程 / 確率過程論 / 確率解析 / 確率微分方程式モデル

Research Abstract

Mainly, we have derived the following results concerning statistical inference for stochastic process models with jumps: (1) Asymptotic normality of the Gaussian quasi-likelihood type estimator together with an easy-to-use approximate confidence regions, when the model has general non-linear coefficients and non-Gaussian noise; (2) Model-free asymptotic distribution of a bias-corrected functional of residuals, with applications to noise-normality and diffusion-coefficient misspecification tests, when the model is of a general continuous-time regression type; (3) Asymptotic mixed normality of the least-absolute deviation estimator and the quasi-likelihood estimator based on the small-time stable approximation, when the noise process can be approximately non-Gaussian stable in small time. In particular, the proposed estimator in (3) is much more efficient than that in (1), while the model setting in (3) is more limited compared with that of (1).

Research Products

• [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, no.4 Pages: 1-51
  • URL: http://www.jstatsoft.org/v57/i04
  • Peer Reviewed
• [Journal Article] Edgeworth expansion for the integrated Levy driven Ornstein-Uhlenbeck process (2013)
  • 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
  • Peer Reviewed
• [Journal Article] Convergence of Gaussian quasi-likelihood random fields for ergodic Levy driven SDE observed at high frequency (2013)
  • Author(s): H. Masuda
  • Journal Title: Annals of Statistics Volume: 41 Issue: 3 Pages: 1593-1641
  • DOI: 10.1214/13-aos1121
  • Peer Reviewed
• [Journal Article] Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes (2013)
  • Author(s): H. Masuda
  • Journal Title: Stochastic Processes and their Applications Volume: 123 Issue: 7 Pages: 2752-2778
  • DOI: 10.1016/j.spa.2013.03.013
  • Peer Reviewed
• [Journal Article] Local asymptotic normality for normal inverse Gaussian Levy processes with high-frequency sampling (2012)
  • Author(s): Reichiro Kawai, H.Masuda
  • Journal Title: ESAIM : Probability and Statistics Volume: (to appear) Pages: 13-32
  • DOI: 10.1051/ps/2011101
  • Peer Reviewed
• [Journal Article] An optimal weight for realized variance based on intermittent high-frequency data (2012)
  • Author(s): Masuda, H. and Morimoto, T
  • Journal Title: Japanese Economic Review Volume: 63 Issue: 4 Pages: 497-527
  • DOI: 10.1111/j.1468-5876.2011.00552.x
  • Peer Reviewed
• [Journal Article] Infinite variation tempered stable Ornstein-Uhlenbeck processes with discrete observations (2012)
  • Author(s): Reichiro Kawai, H.Masuda
  • Journal Title: Communications in Statistics-Simulation and Computation Volume: 41(1) Issue: 1 Pages: 125-139
  • DOI: 10.1080/03610918.2011.582561
  • Peer Reviewed
• [Journal Article] Exact discrete sampling of finite variation tempered stable Ornstein-Uhlenbeck processes (2011)
  • Author(s): Reichiro Kawai, H.Masuda
  • Journal Title: Monte Carlo Methods and Applications Volume: 17(3) Issue: 3 Pages: 279-300
  • DOI: 10.1515/mcma.2011.012
  • Peer Reviewed
• [Journal Article] Goodness of fit test for ergodic diffusions by discrete time observations : an innovation martingale approach (2011)
  • Author(s): Masuda, H., Negri, I., Nishiyama, Y.
  • Journal Title: Journal of Nonparametric Statistics Volume: 23 Issue: 2 Pages: 237-254
  • DOI: 10.1080/10485252.2010.510186
  • Peer Reviewed
• [Journal Article] On the local asymptotic behavior of the likelihood function for Meixner Levy processes under high-frequency sampling (2011)
  • Author(s): Reichiro Kawai, H.Masuda
  • Journal Title: Statistics and Probability Letters Volume: 81(4) Issue: 4 Pages: 460-469
  • DOI: 10.1016/j.spl.2010.12.011
  • Peer Reviewed
• [Journal Article] On simulation of tempered stable random variates (2011)
  • Author(s): Reichiro Kawai, H.Masuda
  • Journal Title: Journal of Computational and Applied Mathematics Volume: 235(8) Issue: 8 Pages: 2873-2887
  • DOI: 10.1016/j.cam.2010.12.014
  • Peer Reviewed
• [Presentation] Remark on the large deviation inequality in mixed-rates asymptotics (2014)
  • Organizer: ASC2014 Asymptotic Statistics and Computations 2014, Graduate School of Mathematical Sciences
  • Place of Presentation: University of Tokyo
  • Year and Date: 2014-03-12
• [Presentation] LAD-based estimation of locally stable Ornstein-Uhlenbeck processes (2014)
  • Organizer: Waseda International Symposium on "Stable Process, Semimartingale, Finance & Pension Mathematics"
  • Place of Presentation: Waseda University
  • Year and Date: 2014-03-04
  • Invited
• [Presentation] LAD-based estimation of locally stable Ornstein-Uhlenbeck processes (2014)
  • Author(s): Hiroki Masuda
  • Organizer: Waseda International Symposium on "Stable Process, Semimartingale, Finance & Pension Mathematics"
  • Place of Presentation: 早稲田大学
  • Invited
• [Presentation] Remark on the large deviation inequality in mixed-rates asymptotics (2014)
  • Author(s): Hiroki Masuda
  • Organizer: Asymptotic Statistics and Computations 2014
  • Place of Presentation: 東京大学
• [Presentation] Stable quasi-likelihood : Methodology and computational aspects (2013)
  • Organizer: ERCIM 2013
  • Place of Presentation: London
  • Year and Date: 2013-12-15
  • Invited
• [Presentation] Multi-step estimation procedure for stable Ornstein-Uhlenbeck processes (2013)
  • Organizer: Stochastic processes and their statistics in Finance
  • Place of Presentation: Okinawa
  • Year and Date: 2013-10-27
  • Invited
• [Presentation] Estimation of jump SDE via local stable approximation (2013)
  • Organizer: Japanese Joint Statistical Meeting 2013
  • Place of Presentation: Osaka University
  • Year and Date: 2013-09-09
  • Invited
• [Presentation] On statistical inference for Levy-driven models (2013)
  • Organizer: ISI 2013
  • Place of Presentation: Hong Kong
  • Year and Date: 2013-08-26
  • Invited
• [Presentation] Estimation of stable-like stochastic differential equations (2013)
  • Organizer: 29th European Meeting of Statisticians
  • Place of Presentation: Eotvos Lorand University, Budapest
  • Year and Date: 2013-07-20
  • Invited
• [Presentation] On optimal estimation of stable Ornstein-Uhlenbeck processes (2013)
  • Organizer: Dynstoch meeting 2013
  • Place of Presentation: University of Copenhagen
  • Year and Date: 2013-04-19
• [Presentation] Toward numerical computation of conditional expectations involving Levy integrals (2013)
  • Organizer: Workshop ASC2013 Asymptotic Statistics and Computations
  • Place of Presentation: University of Tokyo
  • Year and Date: 2013-03-27
• [Presentation] 局所安定分布近似と高頻度データ (2013)
  • Author(s): 増田弘毅
  • Organizer: 統計数学セミナー
  • Place of Presentation: 大阪大学
• [Presentation] Estimation of stable-like stochastic differential equations (2013)
  • Author(s): Hiroki Masuda
  • Organizer: 29th European Meeting of Statisticians
  • Place of Presentation: Eotvos Lorand University
  • Invited
• [Presentation] On statistical inference for Levy-driven models (2013)
  • Author(s): Hiroki Masuda
  • Organizer: International Statistical Institute 2013 Hong Kong
  • Place of Presentation: the Hong Kong Convention and Exhibition Centre
  • Invited
• [Presentation] 局所安定近似による推定方式 (2013)
  • Author(s): 増田弘毅
  • Organizer: 日本統計関連学会連合大会
  • Place of Presentation: 大阪大学
  • Invited
• [Presentation] Multi-step estimation procedure for stable Ornstein-Uhlenbeck processes (2013)
  • Author(s): Hiroki Masuda
  • Organizer: Stochastic processes and their statistics in Finance
  • Place of Presentation: 沖縄青年会館
  • Invited
• [Presentation] Stable quasi-likelihood: Methodology and computational aspects (2013)
  • Author(s): Hiroki Masuda
  • Organizer: ERCIM 2013
  • Place of Presentation: Senate House, University of London
  • Invited
• [Presentation] On simulation of Levy processes and stochastic differential equation models (2012)
  • Organizer: Workshop SART2012 : Statistical Analysis and Related Topics : Theory, Methodology and Data Analysis
  • Place of Presentation: University of Tokyo
  • Year and Date: 2012-12-20
• [Presentation] On asymptotic behavior of self-normalized residual sequence (2012)
  • Organizer: Japanese Joint Statistical Meeting 2012
  • Place of Presentation: Hokkaido University
  • Year and Date: 2012-09-10
  • Invited
• [Presentation] Non-Gaussian quasi-likelihoods for estimating jump SDE (2012)
  • Organizer: 8th World Congress in Probability and Statistics
  • Place of Presentation: Istanbul
  • Year and Date: 2012-07-13
• [Presentation] Non-Gaussian quasi likelihood in estimating jump SDE (2012)
  • Organizer: 2nd APRM
  • Place of Presentation: Epochal Tsukuba
  • Year and Date: 2012-07-03
  • Invited
• [Presentation] Local-stable contrast function (2012)
  • Organizer: Dynstoch meeting 2012
  • Place of Presentation: Institut Henri Poincare, France
  • Year and Date: 2012-06-09
• [Presentation] On self-normalized residuals of stochastic processes (2012)
  • Organizer: Japanese Society of Applied Statistics
  • Place of Presentation: Institute of Statistical Mathematics
  • Year and Date: 2012-05-24
  • Invited
• [Presentation] Asymptotic mixed normality in estimation of jump SDE (2012)
  • Organizer: workshop "Statistics for Stochastic Processes : Inference, Limit Theorems, Finance and Data Analysis"
  • Place of Presentation: Institut Louis Bachelier, Paris
  • Year and Date: 2012-03-13
• [Presentation] Asymptotic mixed normality in estimation of jump SDE (2012)
  • Author(s): Hiroki Masuda
  • Organizer: "Statistics for Stochastic Processes: Inference, Limit Theorems, Finance and Data Analysis"
  • Place of Presentation: Institut Louis Bachelier (France)
• [Presentation] Statistical inference for jump processes (2011)
  • Organizer: workshop "Infinitely divisible processes and related topics"
  • Place of Presentation: The Institute of Statistical Mathematics
  • Year and Date: 2011-11-11
  • Invited
• [Presentation] Very simple estimation of a non-Gaussian process model (2011)
  • Organizer: Forum "Math-for-Industry" 2011
  • Place of Presentation: East-West Center, University of Hawaii
  • Year and Date: 2011-10-28
• [Presentation] On quasi-likelihood analyses for stochastic differential equations with jumps (2011)
  • Organizer: ISI 2011
  • Place of Presentation: Dublin, Ireland
  • Year and Date: 2011-08-26
  • Invited
• [Presentation] On self-normalized residuals of SDE (2011)
  • Organizer: Dynstoch meeting 2011
  • Place of Presentation: University of Heidelberg, Germany
  • Year and Date: 2011-06-16
• [Presentation] On self-normalized residuals of SDE (2011)
  • Author(s): Hiroki Masuda
  • Organizer: Dynstoch meeting 2011(招待講演)
  • Place of Presentation: University of Heiderberg (Germany)
• [Presentation] On quasi-likelihood analyses for stochastic differential equations with jumps (2011)
  • Author(s): Hiroki Masuda
  • Organizer: ISI 2011(招待講演)
  • Place of Presentation: Convention Centre Dublin (Ireland)
• [Presentation] Gaussian quasi likelihood analysis for Levy driven SDE and YUIMA package (2011)
  • Author(s): Hiroki Masuda
  • Organizer: Joint Statistical Meeting
  • Place of Presentation: Kyushu University
• [Presentation] Statistical inference for jump processes (2011)
  • Author(s): Hiroki Masuda
  • Organizer: Workshop "Infinitely divisible processes and related topics"(招待講演)
  • Place of Presentation: The Institute of Statistical Mathematics (Japan), Tokyo
• [Presentation] On self-normalized residuals of stochastic processes
  • Author(s): 増田 弘毅
  • Organizer: 応用統計学会
  • Place of Presentation: 統計数理研究所
  • Invited
• [Presentation] Local-stable contrast function
  • Author(s): Hiroki Masuda
  • Organizer: Dynstoch meeting
  • Place of Presentation: Institut Henri Poincare (France)
• [Presentation] Non-Gaussian quasi likelihood in estimating jump SDE
  • Author(s): Hiroki Masuda
  • Organizer: The 2nd Institute of Mathematical Statistics Asian Pacific Rim Meeting
  • Place of Presentation: エポカルつくば
  • Invited
• [Presentation] Non-Gaussian quasi-likelihoods for estimating jump SDE
  • Author(s): Hiroki Masuda
  • Organizer: 8th World Congress in Probability and Statistics
  • Place of Presentation: Grand Cevahir Hotel and Convention Center (Turkey)
• [Presentation] On asymptotic behavior of self-normalized residual sequence
  • Author(s): 増田 弘毅
  • Organizer: 日本統計関連連合大会
  • Place of Presentation: 北海道大学
  • Invited
• [Presentation] On self-normalized residual sequence of SDE
  • Author(s): 増田 弘毅
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 九州大学
• [Presentation] On simulation of Levy processes and stochastic differential equation models
  • Author(s): 増田 弘毅
  • Organizer: SART2012: Statistical Analysis and Related Topics: Theory, Methodology and Data Analysis
  • Place of Presentation: 東京大学
• [Presentation] Toward numerical computation of conditional expectations involving Levy integrals
  • Author(s): 増田 弘毅
  • Organizer: ASC2013: Asymptotic Statistics and Computations
  • Place of Presentation: 東京大学
• [Presentation] On estimating stable Ornstein-Uhlenbeck processes
  • Author(s): 増田 弘毅
  • Organizer: ASC2013: Asymptotic Statistics and Computations
  • Place of Presentation: 東京大学
• [Remarks] (1) 個人ホームページ ホームページ等
  • URL: https://sites.google.com/site/hm20131017/
• [Remarks] (2) 九州大学研究者情報 ホームページ等
  • URL: http://hyoka.ofc.kyushu-u.ac.jp/search/details/K002496/index.html
• [Remarks] Hiroki Masuda (personal webpage)
  • URL: https://sites.google.com/site/hm20131017/
• [Remarks] 九州大学研究者情報 [増田弘毅]
  • URL: http://hyoka.ofc.kyushu-u.ac.jp/search/details/K002496/index.html