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Applying Spectral Graph Theory to Spatial Econometrics

Research Project

Project/Area Number 20K20759
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 InstitutionHiroshima University

Principal Investigator

YAMADA HIROSHI  広島大学, 人間社会科学研究科(社), 教授 (90292078)

Project Period (FY) 2020-07-30 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2022: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2021: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2020: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywordsスペクトル・グラフ理論 / 空間計量経済学 / グラフ・ラプラシアン / ギアリーのc / モランのI / スペクトルグラフ理論 / 空間自己相関 / HPフィルター / Gearyのc / MoranのI / bHPフィルター / グラフ・フーリエ変換 / 離散コサイン変換 / von Neumann比 / グラフ理論 / グラフラプラシアン / 隣接行列 / グラフフーリエ変換
Outline of Research at the Start

本研究は,空間計量経済学に,スペクトル・グラフ理論[数学の一分野であるグラフ理論の中でもグラフ構造を反映する行列の固有値・固有ベクトルについて研究する学問分野]の知見を持ち込み,空間計量経済分析を発展させることをその目的とする。具体的には,グラフ・フーリエ変換を使った新たな回帰モデルを提案しそれを実用化するための研究を行うほか,空間計量経済分析の代表的モデルである空間自己回帰モデルに現れる空間パラメータに関する理論的な研究を行い成果の獲得を目指す。

Outline of Final Research Achievements

I conducted the research project to advance spatial econometrics using spectral graph theory. As a result, I succeeded in (i) developing a new spatial data smoothing method using the graph Laplacian and clarifying its properties, (ii) obtaining new insights on Geary's c, which is one of the representative spatial autocorrelation measures. In addition, (iii) a quantile version of the Hodrick-Prescott (HP) filter and a hybrid filter of the HP filter and a multiple regression model were developed.

Academic Significance and Societal Importance of the Research Achievements

スペクトル・グラフ理論の知見は,空間計量経済学に十分に活かされているとは言えない状況であった。特に,グラフ・ラプラシアンの活用はほとんどされていなかった。こうした中,本研究は,(i)代表的な空間自己相関指標の一つであるギアリーのcをグラフ・ラプラシアンを使って表現しその性質を明らかにすること,(ii)ギアリーのcに対応する空間スムージングの方法を提案しその性質を明らかにすること,(iii) 新たに導入したスムージング法と重回帰モデルとの混合フィルターを導入すること,などにより空間計量経済学を発展させることに貢献した。

Report

(5 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (16 results)

All 2024 2023 2022 2021 2020

All Journal Article (6 results) (of which Peer Reviewed: 6 results,  Open Access: 3 results) Presentation (10 results) (of which Int'l Joint Research: 7 results,  Invited: 2 results)

  • [Journal Article] Spatial Smoothing Using Graph Laplacian Penalized Filter2024

    • Author(s)
      Yamada Hiroshi
    • Journal Title

      Spatial Statistics

      Volume: 60 Pages: 100799-100799

    • DOI

      10.1016/j.spasta.2023.100799

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] HPX filter: a hybrid of Hodrick-Prescott filter and multiple regression2023

    • Author(s)
      Yamada Hiroshi
    • Journal Title

      Studies in Nonlinear Dynamics and Econometrics

      Volume: - Issue: 4 Pages: 661-671

    • DOI

      10.1515/snde-2023-0004

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A unified perspective on some autocorrelation measures in different fields: A note2023

    • Author(s)
      Yamada Hiroshi
    • Journal Title

      Open Mathematics

      Volume: 21 Issue: 1

    • DOI

      10.1515/math-2022-0574

    • Related Report
      2023 Annual Research Report 2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Quantile regression version of Hodrick-Prescott filter2022

    • Author(s)
      Hiroshi Yamada
    • Journal Title

      Empirical Economics

      Volume: - Issue: 4 Pages: 1631-1645

    • DOI

      10.1007/s00181-022-02292-8

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Geary’s c and Spectral Graph Theory2021

    • Author(s)
      Yamada Hiroshi
    • Journal Title

      Mathematics

      Volume: 9 Issue: 19 Pages: 2465-2465

    • DOI

      10.3390/math9192465

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A pioneering study on discrete cosine transform2020

    • Author(s)
      Yamada Hiroshi
    • Journal Title

      Communications in Statistics - Theory and Methods

      Volume: - Issue: 15 Pages: 5364-5368

    • DOI

      10.1080/03610926.2020.1838547

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Presentation] Spatial Smoothing Using Graph Laplacian Penalized Filter2023

    • Author(s)
      山田宏
    • Organizer
      The 25th International Conference on Computational Statistics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Spatial Smoothing Using Graph Laplacian Penalized Filter2023

    • Author(s)
      山田宏
    • Organizer
      Spatial Statistics 2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Spatial Smoothing Using Graph Laplacian Penalized Filter2023

    • Author(s)
      山田宏
    • Organizer
      The 17th International Symposium on Econometric Theory and Applications
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Unified Perspective on the Simple and Boosted HP Filters and the Results Derived from It2023

    • Author(s)
      Hiroshi Yamada
    • Organizer
      SH3 Conference on Econometrics 2023
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Nonnegative Definite Matrix Penalized Filtering with Quantile Regression Loss Function2023

    • Author(s)
      Hiroshi Yamada
    • Organizer
      第30回関西計量経済学研究会
    • Related Report
      2022 Research-status Report
  • [Presentation] Spatial Filtering2022

    • Author(s)
      山田宏
    • Organizer
      第29回関西計量経済学研究会
    • Related Report
      2021 Research-status Report
  • [Presentation] Seasonal Filtering2022

    • Author(s)
      山田宏
    • Organizer
      The SH3 Virtual Conference on Econometrics
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] Spatial Autocorrelation and Spectral Graph Theory2021

    • Author(s)
      山田宏
    • Organizer
      The Applied Statistics Workshop 2021 (東京大学)
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Spatial Autocorrelation and Spectral Graph Theory2021

    • Author(s)
      山田宏
    • Organizer
      SH3 Conference on Econometrics 2021
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] Spatial Autocorrelation and Spectral Graph Theory2021

    • Author(s)
      山田宏
    • Organizer
      2021 Nanyang Econometrics Conference
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research

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Published: 2020-08-03   Modified: 2025-01-30  

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