New developments from heteroskedastic models in non-negative integer-valued time series analysis

• Project/Area Number: 21K20338
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 0201:Algebra, geometry, analysis, applied mathematics,and related fields
• Research Institution: Kyushu University (2022); Waseda University (2021)
• Principal Investigator: Goto Yuichi 九州大学, 数理学研究院, 助教 (90907073)
• Project Period (FY): 2021-08-30 – 2023-03-31
• Project Status: Completed (Fiscal Year 2022)
• Budget Amount: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2022: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 計数時系列 / 分散不均一性 / 一致性 / 漸近正規性 / M-推定 / 数理統計学

Outline of Research at the Start

計数時系列とは、非負整数値の時系列データのことである。近年、計数時系列に対する研究が盛んにされているが、既存研究では、極めて限定的な場合のみでしか、分散不均一性を表現することが出来ない。本研究では、計数時系列に対して、ARMA-GARCHモデルの構造を取り入れることで、分散不均一性を表現することを目指す。これにより、モデリングの幅が格段に広がる。具体的には、地震の発生確率の推定、株価取引回数に基づく金融危機の事前察知、感染症患者数の予測等々の広汎な現象の解明やSNSにおける投稿のお気に入り回数と引用回数を用いた炎上のメカニズムの解析など「全く新しい分野の計数データ」を用いた解析に繋がる。

Outline of Final Research Achievements

In this project, we proposed a model that incorporates an autoregressive structure not only for the conditional expectation but also for the conditional variance in order to introduce a model corresponding to the ARMA-GARCH model to counted time series analysis. The unknown parameters of this model can be estimated in two steps, and their consistency and asymptotic normality are proved. We found that the model can be applied to other testing problems that have not been proposed before. Although we had struggled to show the stationarity of the model, we were able to find clues. These contents will be submitted to an international journal as soon as they are ready. In addition, four papers were published in international journals and presented at domestic and international conferences.

Academic Significance and Societal Importance of the Research Achievements

本研究成果の学術的意義として, 計数時系列のモデリングの柔軟性が広がることが挙げられる。実際、ARMA-GARCH モデルは, 実証研究にも用いられている実用的なモデルである。さらに、条件付き分散不均一性がINGARCHモデルでは正しく表現できていないため、条件付き分散不均一性を正しく考慮したモデルであるという点にも学術的な価値がある. 研究期間中に出版した論文のうちのひとつは, 統計のトップジャーナルである.

Research Products

• [Int'l Joint Research] University of Toronto(カナダ)
• [Int'l Joint Research] Georg-August-Universitat Gottingen/Ruhr-Universitat Bochum(ドイツ)
• [Int'l Joint Research] Universite libre de Bruxelles(ベルギー)
• [Int'l Joint Research] Wuhan University(中国)
• [Int'l Joint Research] Universite libre de Bruxelles(ベルギー)
• [Int'l Joint Research] Ruhr-Universitat Bochum/Georg August University of Gottingen(ドイツ)
• [Int'l Joint Research] University of Toronto(カナダ)
• [Int'l Joint Research] National University of Singapore(シンガポール)
• [Journal Article] Tests for a structural break for non-negative integer-valued time series (2023)
  • Author(s): Goto Yuichi
  • Journal Title: Research Papers in Statistical Inference for Time Series and Related Models: Essays in Honor of Masanobu Taniguchi Volume: -
  • Peer Reviewed
• [Journal Article] The integrated copula spectrum (2022)
  • Author(s): Goto Yuichi、Kley Tobias、Van Hecke Ria、Volgushev Stanislav、Dette Holger、Hallin Marc
  • Journal Title: The Annals of Statistics Volume: 50 Issue: 6 Pages: 3563-3591
  • DOI: 10.1214/22-aos2240
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Tests for the existence of group effects and interactions for two-way models with dependent errors (2022)
  • Author(s): Goto Yuichi、Suzuki Kotone、Xu Xiaofei、Taniguchi Masanobu
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: 75 Issue: 3 Pages: 511-532
  • DOI: 10.1007/s10463-022-00853-3
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Homogeneity tests for one-way models with dependent errors under correlated groups (2022)
  • Author(s): Goto Yuichi、Arakaki Koichi、Liu Yan、Taniguchi Masanobu
  • Journal Title: TEST Volume: 32 Issue: 1 Pages: 163-183
  • DOI: 10.1007/s11749-022-00828-9
  • Peer Reviewed / Open Access
• [Presentation] Integrated copula spectrum with applications to tests for time-reversibility and tail symmetry (2023)
  • Author(s): Y. Goto, Kley, T., Hecke, R. V., Volgushev, S, Dette, H., Hallin, M.
  • Organizer: Data Science Workshop, Tohoku University.
  • Invited
• [Presentation] The existence and uniqueness of lagged spectrum (2023)
  • Author(s): Y. Goto, X. Zhang, B. Kedem, S. Chen
  • Organizer: Kanazawa Seminar, Hotel Kanazawa
  • Int'l Joint Research / Invited
• [Presentation] A subsampling-based test to detect interregional differences among small-sample time series in marine study (2023)
  • Author(s): Y. Goto, H.K. Solvang, M. Taniguchi
  • Organizer: IMR-Waseda Workshop, Advances in pragmatic computational methodologies for fish stock assessment, human impact, and environmental factor on marine ecosystems, Institute of Marine Research
  • Int'l Joint Research / Invited
• [Presentation] ests for the existence of group effects and interactions for two-way models with depend-ent error (2022)
  • Author(s): Y. Goto, X. Xu, K. Suzuki., and M. Taniguchi
  • Organizer: Mathematical Society of Japan Spring Meeting 2022
• [Presentation] time series analysis related to spectra (2022)
  • Author(s): Y. Goto
  • Organizer: Statistics Seminar, Kyushu Univ.
  • Invited
• [Presentation] Integrated copula spectrum with applications to tests for time-reversibility and tail symmetry (2022)
  • Author(s): Y. Goto, Kley, T., Hecke, R. V., Volgushev, S, Dette, H., Hallin, M.
  • Organizer: Mathematical Society of Japan Autumn Meeting 2022, Hokkaido Univ., Special lecture
  • Invited
• [Presentation] Likelihood Ratio Processes under Non-Standard Settings (2022)
  • Author(s): Y. Goto, T. Kaneko, S. Kojima, M. Taniguchi
  • Organizer: Waseda mini-workshop, Recent development on time series analysis and related topics, Waseda Univ.
  • Invited
• [Presentation] Homogeneity tests for one-way models with dependent errors under correlated groups (2022)
  • Author(s): Y. Goto, K. Arakaki, Y. Liu, and M. Taniguchi
  • Organizer: Waseda International Symposium “Topological Data Science, Causality, Analysis of Variance & Time Series” dedicated to Professor Taniguchi's retirement, Waseda University.
  • Int'l Joint Research / Invited
• [Presentation] Tests for the existence of group effects and interactions for two-way models with dependent errors (2022)
  • Author(s): Y. Goto, Suzuki. K., Xu, X., and M. Taniguchi
  • Organizer: Otsu Seminar “Recent Developments in Time Series and Related Topics” In honor of Professor Masanobu Taniguchi on the occasion of his retirement, Biwako Hotel.
  • Int'l Joint Research / Invited
• [Presentation] Discriminant analysis based on binary time series (2022)
  • Author(s): Y. Goto, M. Taniguchi
  • Organizer: The 5th International Conference on Econometrics and Statistics, Ryukoku University.
  • Int'l Joint Research / Invited
• [Presentation] Integrated copula spectrum with applications to tests for time-reversibility and tail symmetry (2022)
  • Author(s): Y. Goto, Kley, T., Hecke, R. V., Volgushev, S, Dette, H., Hallin, M.
  • Organizer: Rome-Waseda Time Series Symposium, Tor Vergata University of Rome
  • Int'l Joint Research / Invited
• [Presentation] Integrated copula spectrum with applications to tests for time-reversibility and tail symmetry (2022)
  • Author(s): Y. Goto, Kley, T., Hecke, R. V., Volgushev, S, Dette, H., Hallin, M.
  • Organizer: Statistics Seminar, University of Maryland
  • Int'l Joint Research / Invited
• [Presentation] Homogeneity tests for one-way models with dependent errors under correlated groups (2022)
  • Author(s): Y. Goto, K. Arakaki, Y. Liu, and M. Taniguchi
  • Organizer: Bologna-Waseda Time Series Workshop, University of Bologna
  • Int'l Joint Research / Invited
• [Presentation] Tests for the existence of group effects and interactions for two-way models with dependent error (2022)
  • Author(s): Y. Goto, K. Suzuki, X. Xu, and M. Taniguchi
  • Organizer: Mathematical Society of Japan Spring Meeting 2022. Saitama Univ.
• [Presentation] Tests for the existence of group effects and interactions for two-way models with dependent errors (2022)
  • Author(s): Y. Goto, K. Suzuki, X. Xu, and M. Taniguchi
  • Organizer: Otsu Seminar “Recent Developments in Time Series and Related Topics” In honor of Professor Masanobu Taniguchi on the occasion of his retirement, Biwako Hotel.
  • Int'l Joint Research / Invited
• [Presentation] Homogeneity tests for one-way models with dependent errors under correlated groups (2022)
  • Author(s): Y. Goto, K. Arakaki, Y. Liu, and M. Taniguchi
  • Organizer: Waseda International Symposium “Topological Data Science, Causality, Analysis of Variance & Time Series” dedicated to Professor Taniguchi's retirement, Waseda Uni-versity.
  • Int'l Joint Research / Invited
• [Presentation] Homogeneity tests for one-way models with dependent errors (2021)
  • Author(s): Y. Goto, K. Arakaki, Y. Liu, and M. Taniguchi
  • Organizer: Mathematical Society of Japan Autumn Meeting 2021. Online
• [Presentation] Hypothesis tests for one- and two-way models with dependent errors (2021)
  • Author(s): Y. Goto, K. Arakaki, K. Suzuki, X. Xu, Y. Liu, and M. Taniguchi
  • Organizer: Data Science Workshop, Tohoku University.
  • Invited
• [Remarks] 個人ホームページ
  • URL: https://www2.math.kyushu-u.ac.jp/~yuichi.goto/