Statistical Sequential Analysis of Non-stationary Time Series using Stopping Times Based on Information

• Project/Area Number: 18K01543
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 07030:Economic statistics-related
• Research Institution: Yokohama National University
• Principal Investigator: Nagai Keiji 横浜国立大学, 大学院国際社会科学研究院, 教授 (50311866)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 非エルゴード的問題 / 自己回帰過程 / 単位根検定 / 分枝過程 / 臨界性検定 / 観測されたフィッシャー情報量 / 結合ラプラス変換 / ベッセル過程 / モニタリング / 非エルゴード性 / 停止時刻 / フィッシャー情報量 / 一様最強力検定 / 逐次解析 / Bessel過程 / Bessel bridge / 結合密度関数 / 時間変更 / オンラインモニタリング / 経済・金融時系列 / ブラウン運動 / 汎関数中心極限定理 / 非定常時系列解析 / 統計的逐次解析 / 情報量 / 非線形定常時系列

Outline of Final Research Achievements

In order to quickly detect emergencies such as bubbles and disease outbreaks, we developed sequential unit root tests for autoregressive processes and sequential criticality tests for branching processes with and without immigration. Using stopping times based on observed Fisher information, we derived Z-tests (tests based on normal distribution) for hypotheses involving explosive cases. The joint limit of the stopping time and the sequential Z-test is characterized by a 3/2-dimensional Bessel process driven by time-changed Brownian motion. the Z-test was found to be the uniformly most powerful invariant sequential test. We also provided some sequential tests reducing sampling cost under stable alternatives and detecting explosive states quickly.

Academic Significance and Societal Importance of the Research Achievements

非エルゴード的問題とされる自己回帰過程に対する単位根検定と、移民項を含む場合と含まない場合の分枝過程に対する臨界性検定に対し，観測されたフィッシャー情報に基づく停止時刻を用いて逐次解析の手法を提案した．局所仮説（安定的な場合と爆発的な場合を含む）に対するZ検定を導出した。停止時間と逐次Z検定の結合極限は、時間変更されたブラウン運動によって駆動される3/2次元ベッセル過程で特徴づけられ，結合分布および同時結合ラプラス変換を数学的に求めた．Z検定は最強力不変逐次検定であることがわかり、安定的な対立仮説の下でサンプリングコストを削減し、爆発状態を迅速に検出するいくつかの逐次検定を提供した。

Research Products

• [Journal Article] Sequential tests for criticality of branching process with immigration (2021)
  • Author(s): J. Tao, K. Nagai
  • Journal Title: Discussion Paper Series, Center for Economic Growth Strategy, Yokohama National University Volume: 2020-CEGS-05 Pages: 1-14
  • Open Access
• [Presentation] Detection of a unit root in monitoring AR(p) process with combination of a sequential procedure and the augmented Dickey-Fuller test (2021)
  • Author(s): Keiji Nagai
  • Organizer: The 28th Kansai Keiryo Keizaigaku Kenkyukai(関西計量経済学研究会)
• [Presentation] Operating characteristics of sequential unit root tests obtained from the Bessel bridges (2020)
  • Author(s): Keiji Nagai
  • Organizer: Bernoulli-IMS, One World Symposium
  • Int'l Joint Research
• [Presentation] Sequential test for the criticality of branching processes (2020)
  • Author(s): Keiji Nagai
  • Organizer: Japan Joint Statistical Meeting (統計関連学会連合大会)
  • Int'l Joint Research
• [Presentation] Monitoring Unit Root in Sequentially Observed Autoregressive Processes against Local-to-unity hypotheses”, (2019)
  • Author(s): [1]K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao
  • Organizer: 62nd ISI World Statistics Congress 2019, International Statistical Institute
  • Int'l Joint Research
• [Presentation] Joint Asymptotic Normality of Stopping Times and Sequential Estimators in Monitoring Autoregressive Processes (2019)
  • Author(s): K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao
  • Organizer: 62nd ISI World Statistics Congress 2019, International Statistical Institute
  • Int'l Joint Research
• [Presentation] Sequential Unit Root Test (2019)
  • Author(s): Y. Nishiyama, Kohtaro Hitomi, Keiji Nagai
  • Organizer: Workshop on Recent Progress in Time Series in honour of Peter Robinson
  • Int'l Joint Research / Invited
• [Presentation] The relationship between Dickey-Fuller test and Sequential unit root test for first-order autoregressive model (2019)
  • Author(s): K. Nagai, K. Hitomi, Y. Nishiyama, J. Tao
  • Organizer: 2019年度統計関連学会連合大会 / Japanese joint statistical meeting 2019
• [Presentation] Sequential detection of the order of integration for pth-order autoregressive mode (2019)
  • Author(s): K. Nagai, Y. Nishiyama, K. Hitomi, J. Tao
  • Organizer: 2019年度統計関連学会連合大会 / Japanese joint statistical meeting 2019
• [Presentation] Sequential Estimation for Strongly Stationary AR(p) Process (2018)
  • Author(s): Junfan Tao
  • Organizer: 日本統計関連連合大会
• [Presentation] Sequential Unit Root Test in AR(p) Model (2018)
  • Author(s): Keiji Nagai
  • Organizer: 日本統計関連連合大会
• [Remarks] 横浜国立大学が取り組む新型コロナウイルスに係る研究事例について
  • URL: https://www.ynu.ac.jp/special/topic/research01.html