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経済時系列の逐次統計解析とその応用~金融バブルの検出

Research Project

Project/Area Number 19K21691
Research Category

Grant-in-Aid for Challenging Research (Exploratory)

Allocation TypeMulti-year Fund
Review Section Medium-sized Section 7:Economics, business administration, and related fields
Research InstitutionKyoto University

Principal Investigator

西山 慶彦  京都大学, 経済研究所, 教授 (30283378)

Co-Investigator(Kenkyū-buntansha) 人見 光太郎  京都工芸繊維大学, 基盤科学系, 教授 (00283680)
永井 圭二  横浜国立大学, 大学院国際社会科学研究院, 教授 (50311866)
Project Period (FY) 2019-06-28 – 2023-03-31
Project Status Granted (Fiscal Year 2021)
Budget Amount *help
¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2021: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2020: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2019: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywords逐次解析 / 単位根検定 / 臨界性検定 / criticality test / 自己回帰モデル / 分枝過程 / 時系列モデル
Outline of Research at the Start

本研究は、経済時系列分析に逐次解析法を取り入れた統計解析法を構築することである。それにより、例えば金融バブルの発生を早期に検出する方法を確立することが可能になる。データ収集をやめる時点を停止時といい、本研究では自己回帰モデルについて、データの情報の量的指標であるフィッシャー情報量が一定水準Cに達した時点でサンプリングを止める停止時を考える。漸近論ではそのCを大きくする枠組みで、推定問題、単位根検定問題を取り扱い、それらの推定量や検定統計量と停止時の同時分布を導出する。検定問題では、帰無分布のみならず対立分布も導出する。応用例として、金融市場におけるバブルの早期検出が考えられる。

Outline of Annual Research Achievements

本研究では時系列の単位根過程と爆発的な過程,分枝過程の臨界的と優臨界的な状況のような非定常過程のように,Fisher情報量(条件付きFisher情報量)の極限にランダムネスが残る場合,統計学において,非エルゴ―ド的な確率過程と呼ぶ。2021年度日本経済学会秋季大会の「バブルと感染爆発 - 非エルゴード的時系列の検出」という企画セッションを立て,3つの報告でバブルや感染爆発といった非エルゴード的な状態が起こりうる時系列が観測されるときの計量経済学的手法について議論した。
特に、経済時系列モデルとしてよく用いられる自己回帰モデルと疫学で個体数の記述に用いられるGalton-Watson分枝過程における統計的逐次検定の理論研究を行った。前者では,観測されたFisher情報に基づく停止時間を用いた逐次サンプリング方式における次数pの自己回帰過程に対する単位根検定、後者では同様の枠組みの下で基本再生産数に関する臨界性の検定問題を扱った。 それぞれについて、検定統計量と停止時間の同時極限を導出し,DDSブラウン運動によって駆動されるBessel過程を用いて特徴づけられた。また,帰無仮説と局所対立仮説の下で、極限での同時ラプラス変換と同時密度関数を求めた。
AR(p)モデルの逐次単位根検定の論文は学術誌「Advances in Econometrics: Essays in Honor of Joon Y. Park」にアクセプトされた。

Current Status of Research Progress
Current Status of Research Progress

3: Progress in research has been slightly delayed.

Reason

論文投稿に向けての作業が少し遅れているが、それ以外は順調である。

Strategy for Future Research Activity

理論面ではほぼ完成しており、数値計算その他、細かい点を確認して論文として完成させ、国際学術誌に投稿予定である。

Report

(3 results)
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report

Research Products

(18 results)

All 2022 2021 2020 2019

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (17 results) (of which Int'l Joint Research: 7 results)

  • [Journal Article] Sequential test for a unit root in monitoring a p-th order autoregressive process2022

    • Author(s)
      Kohtaro Hitomi, Keiji Nagai, Yoshihiko Nishiyama, and Junfan Tao
    • Journal Title

      Advances in Econometrics: Essays in Honor of Joon Y. Park

      Volume: 1 Pages: 1-31

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Presentation] Sequential criticality test for branching process with immigration2021

    • Author(s)
      Kohtaro Hitomi, Keiji Nagai, Yoshihiko Nishiyama, and Junfan Tao
    • Organizer
      63rd ISI World Statistics Congress 2021 (ISI WSC 2021) (Online)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sequential test for a unit root in monitoring a p-th order autoregressive process2021

    • Author(s)
      Kohtaro Hitomi, Keiji Nagai, Yoshihiko Nishiyama, and Junfan Tao
    • Organizer
      2021 Japanese Economic Association Spring Meeting
    • Related Report
      2021 Research-status Report
  • [Presentation] Criticality test for branching processes with immigration2021

    • Author(s)
      Kohtaro Hitomi, Keiji Nagai, Yoshihiko Nishiyama, and Junfan Tao
    • Organizer
      Japanese joint statistical meeting 2021
    • Related Report
      2021 Research-status Report
  • [Presentation] Time-changed method in non-ergodic autoregressive process and branching process2021

    • Author(s)
      Kohtaro Hitomi, Keiji Nagai, Yoshihiko Nishiyama, and Junfan Tao
    • Organizer
      2021 Japanese Economic Association Autumn Meeting
    • Related Report
      2021 Research-status Report
  • [Presentation] Sequential Test for Unit Root in First Order Autoregressive Model2021

    • Author(s)
      Kohtaro Hitomi, Keiji Nagai, Yoshihiko Nishiyama, and Junfan Tao
    • Organizer
      2021 Japanese Economic Association Autumn Meeting
    • Related Report
      2021 Research-status Report
  • [Presentation] Sequential Test for the Criticality of Branching Processes,2021

    • Author(s)
      Kohtaro Hitomi, Keiji Nagai, Yoshihiko Nishiyama, and Junfan Tao
    • Organizer
      2021 Japanese Economic Association Autumn Meeting
    • Related Report
      2021 Research-status Report
  • [Presentation] Sequential analysis on branching process with immigration with a stopping time based on the observed Fisher information2021

    • Author(s)
      K.Nagai, K. Hitomi, Y.Nishiyama, and J. Tao
    • Organizer
      関西計量経済学研究会
    • Related Report
      2020 Research-status Report
  • [Presentation] Detection of a unit root in monitoring AR(p) process with combination of a sequential procedure and the augmented Dickey-Fuller test2021

    • Author(s)
      K.Nagai, K. Hitomi, Y.Nishiyama, and J. Tao
    • Organizer
      関西計量経済学研究会
    • Related Report
      2020 Research-status Report
  • [Presentation] Operating characteristics of sequential unit root tests obtained from the Bessel bridges2020

    • Author(s)
      K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao.
    • Organizer
      Bernoulli-IMS One World Symposium
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] The role of Bessel processes on the sequential test for a unit root in autoregressive process and criticality in branching processes2020

    • Author(s)
      K.Nagai, K. Hitomi, Y.Nishiyama and J. Tao
    • Organizer
      Bernoulli-IMS One World Symposium
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sequential test for the criticality of branching processes2020

    • Author(s)
      K.Nagai, K. Hitomi, Y.Nishiyama and J. Tao
    • Organizer
      統計連合大会
    • Related Report
      2020 Research-status Report
  • [Presentation] The role of Bessel processes on the sequential test for a unit root in autoregressive process and criticality in branching process2020

    • Author(s)
      K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao
    • Organizer
      統計連合大会
    • Related Report
      2020 Research-status Report
  • [Presentation] Statistical Sequential Analysis of Autoregressive Processes2019

    • Author(s)
      K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao.
    • Organizer
      Data Science Seminar, Shiga University
    • Related Report
      2019 Research-status Report
  • [Presentation] Monitoring Unit Root in Sequentially Observed Autoregressive Processes against Local-to-unity hypotheses2019

    • Author(s)
      K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao.
    • Organizer
      62nd ISI World Statistics Congress 2019 (ISI WSC 2019), Kuala Lumpur, Malaysia
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Joint Asymptotic Normality of Stopping Times and Sequential Estimators in Monitoring Autoregressive Processes2019

    • Author(s)
      K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao.
    • Organizer
      62nd ISI World Statistics Congress 2019 (ISI WSC 2019), Kuala Lumpur, Malaysia
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] The relationship between Dickey-Fuller test and Sequential unit root test for first-order autoregressive model2019

    • Author(s)
      K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao.
    • Organizer
      Japanese joint statistical meeting 2019, Shiga University
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sequential Unit Root Test2019

    • Author(s)
      K.Nagai, Y.Nishiyama, K. Hitomi, and J. Tao.
    • Organizer
      Econometrics Symposium in honor of Peter M. Robinson
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research

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Published: 2019-07-04   Modified: 2022-12-28  

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