Statistical theory for the analysis of long-memory financial time series using continuous-time models

• Project/Area Number: 24530224
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Economic statistics
• Research Institution: Gakushuin University (2013-2015); Hitotsubashi University (2012)
• Principal Investigator: Tanaka Katsuto 学習院大学, 経済学部, 教授 (40126595)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 連続時間確率過程 / Hurst パラメータ / 最尤推定量 / フラクショナル・モデル / エルゴード的な場合 / 非エルゴード的な場合 / 特性関数 / 数値積分 / Fractional O-U process / 非エルゴード性 / ギルサノフの定理 / 極限分布 / フラクショナル O-U モデル / ergodic case / フラクショナル・ブラウン運動 / 確率過程 / O-U 過程 / フラクショナル・Brown 運動

Outline of Final Research Achievements

We investigated the estimation problem for the drift parameter α in the fO-U (fractional Ornstein-Uhlenbeck) process which is a long-memory continuous-time stochastic process.Numerical integration was employed to compute the probability density of the MLE and the density was graphically presented. Asymptotic theory was also developed as the time span goes to infinity. It was proved that the MLE for the non-ergodic case converges to Cauchy distribution. The distribution depends on the Hurst parameter H and is symmetric around H=1/2. It was aslo proved that the concentration probability increases as H gets away from 1/2. These results were published in international refereed journals.

Research Products

• [Journal Article] Maximum likelihood estimation for the non-ergodic fractional Ornstein-Uhlenbeck process (2015)
  • Author(s): Katsuto Tanaka
  • Journal Title: Statistical Inference for Stochastic Processes Volume: 18 Issue: 3 Pages: 315-332
  • DOI: 10.1007/s11203-014-9110-9
  • Peer Reviewed / Open Access
• [Journal Article] Linear Nonstationary Models - A Review of the Work of Professor P.C.B. Phillips (2014)
  • Author(s): Tanaka, K.
  • Journal Title: Econometric Theory Volume: 30 Issue: 4 Pages: 815-838
  • DOI: 10.1017/s0266466613000480
  • Peer Reviewed
• [Journal Article] Distiburions of Quadratic Functionals of the Fractional Brownian Motion Based on A Martingale Approximation (2014)
  • Author(s): Tanak, K.
  • Journal Title: Econometric Theory Volume: 30 Pages: 1078-1109
  • Peer Reviewed
• [Journal Article] Distributions of the Maximum Likelihood and Minimum Contrast Estimators Associated with the Fractional Ornstein-Uhlenbeck Process (2013)
  • Author(s): Katsuto Tanaka
  • Journal Title: Statistical Inference for Stochastic Processes Volume: 16 Issue: 3 Pages: 173-192
  • DOI: 10.1007/s11203-013-9085-y
  • Peer Reviewed
• [Presentation] Limiting local powers of panel unit root tests (2016)
  • Author(s): Katsuto Tanaka
  • Organizer: SETA Meeting
  • Place of Presentation: Hamilton (New Zealand)
  • Year and Date: 2016-02-17
  • Int'l Joint Research
• [Presentation] Statistical analysis of long-memory processes associated with the fractional Brownian motion (2015)
  • Author(s): Tanaka, K.
  • Organizer: 統計学セミナー
  • Place of Presentation: オーストラリア国立大学（キャンベラ）
  • Year and Date: 2015-03-03
• [Presentation] Maximum likelihood estimation for the non-ergodic fractional Ornstein-Uhlenbeck process (2014)
  • Author(s): Tanaka, K.
  • Organizer: 確率論セミナー
  • Place of Presentation: メーヌ大学（フランス，ルマン）
  • Year and Date: 2014-09-04
• [Presentation] Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein-Uhlenbeck process (2014)
  • Author(s): Tanaka, K.
  • Organizer: Waseda International Symposium
  • Place of Presentation: 早稲田大学
  • Invited
• [Presentation] Distributions of quadratic functionals of the fractional Brownian motion based on a martingale approximation
  • Author(s): Tanaka, K.
  • Organizer: ヘルシンキ大学数学科確率論セミナー
  • Place of Presentation: ヘルシンキ大学（フィンランド）
• [Presentation] The non-ergodic fractional Ornstein-Uhlenbeck process and the maximum likelihood estimation
  • Author(s): Tanaka, K.
  • Organizer: ANU Research Seminar
  • Place of Presentation: オーストラリア国立大学（オーストラリア）
• [Presentation] Distributions of quadratic functionals of the fractional Brownian motion based on a martingale approximation
  • Author(s): 田中 勝人
  • Organizer: APRM satellite meeting
  • Place of Presentation: 早稲田大学
• [Presentation] Distributions of quadratic functionals of the fractional Brownian motion based on a martingale approximation
  • Author(s): 田中 勝人
  • Organizer: Probability Seminar
  • Place of Presentation: カンザス大学（米国）
• [Presentation] Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein-Uhlenbeck process
  • Author(s): 田中 勝人
  • Organizer: 韓国との二国間共同セミナー
  • Place of Presentation: 西江大学（韓国）
• [Presentation] Statistical inference associated with the fractional Brownian motion and related processes
  • Author(s): 田中 勝人
  • Organizer: ANU Research Seminar
  • Place of Presentation: オーストラリア国立大学（オーストラリア）