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Sparse statistical approach for multivariate modelling

Research Project

Project/Area Number 22K13377
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 07030:Economic statistics-related
Research InstitutionOsaka University

Principal Investigator

POIGNARD BENJAMIN  大阪大学, 大学院経済学研究科, 准教授 (40845252)

Project Period (FY) 2022-04-01 – 2025-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2024: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2023: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2022: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
KeywordsCopula / Factor model / High dimension / Sparsity / Asymptotic theory / Copulas / Factor models / Time series / Multivariate modelling
Outline of Research at the Start

The research is devoted to the development of sparsity based estimation procedure to tackle the curse of dimensionality. A significant work will be dedicated to the theoretical properties (large sample, finite sample) and the applications (simulations, real world data) to illustrate the relevance of the proposed sparse methods. We expect to greatly enhance the prediction performances of the fitted sparse models. The key challenge is to break the curse of dimensionality inherent to multivariate models.

Outline of Annual Research Achievements

The paper "Sparse M-estimators in semi-parametric copula models", co-authored with Prof Fermanian, has been accepted for publication at Bernoulli in 2023 and is forthcoming in 2024. The paper answered the issues inherent to copula models: pseudo-observations; unbounded copula-based objective functions; explosive number of parameters. We specified a suitable penalized M-estimator framework for copulas and derived the asymptotic properties.
The paper "Sparse factor models of high dimension", co-authored with Prof Terada, is currently submitted at an econometrics journal: we devised a sparsity-based estimation framework for the factor loading matrix taking into account the rotational indeterminacy and derived the asymptotic properties.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

The research is moving forward: one paper published in Bernoulli; one paper currently submitted at an econometrics journals; one research project on stochastic volatility models is about to be completed.

Strategy for Future Research Activity

The project "Factor Multivariate Stochastic Volatility Models", co-authored with Prof Asai, is about to be completed and will be submitted at an econometrics journal. The key idea is to integrate factors in the Multivariate Stochastic Volatility (MSV) model. We propose to estimate the latent factors using the estimators of the factor decomposition and then specify a multivariate state space representation of the latent volatility of the factors (not the observed random vector, which can be high-dimensional). Theoretical analysis of the proposed method: asymptotic properties derived under moment conditions.
The replication package will be made publicly available for the sake of transparancy.

Report

(2 results)
  • 2023 Research-status Report
  • 2022 Research-status Report
  • Research Products

    (9 results)

All 2024 2023 2022

All Journal Article (2 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 2 results,  Open Access: 1 results) Presentation (7 results) (of which Int'l Joint Research: 4 results,  Invited: 3 results)

  • [Journal Article] Sparse M-estimators in semi-parametric copula models2024

    • Author(s)
      Benjamin Poignard and Jean-David Fermanian
    • Journal Title

      Bernoulli

      Volume: Forthcoming

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Estimation of high-dimensional vector autoregression via sparse precision matrix2023

    • Author(s)
      Poignard Benjamin、Asai Manabu
    • Journal Title

      The Econometrics Journal

      Volume: -- Issue: 2 Pages: 307-326

    • DOI

      10.1093/ectj/utad003

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Factor multivariate stochastic volatility models2024

    • Author(s)
      Benjamin Poignard
    • Organizer
      CREST (ENSAE Paris - IP Paris) - Finance & Financial Econometrics Seminar
    • Related Report
      2023 Research-status Report
    • Invited
  • [Presentation] Sparse M-estimator in semi-parametric copula models2023

    • Author(s)
      Benjamin Poignard
    • Organizer
      共同研究集会2023:接合関数(コピュラ)理論の新展開 - 統計数理研究所
    • Related Report
      2023 Research-status Report
    • Invited
  • [Presentation] Sparse factor model of high dimension2023

    • Author(s)
      Benjamin Poignard
    • Organizer
      10th International Congress on Industrial and Applied Mathematics - ICIAM 2023
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sparse factor models of high dimension2022

    • Author(s)
      Benjamin Poignard
    • Organizer
      CFE-CMStatistics 2022 Conference
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sparse M-estimator in semi-parametric copula models2022

    • Author(s)
      Benjamin Poignard
    • Organizer
      The 16th International Symposium on Econometric Theory and Applications: SETA2022
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] Asymptotic theory of sparse factor models in high-dimension2022

    • Author(s)
      Benjamin Poignard
    • Organizer
      International Conference on Econometrics and Statistics (EcoSta 2022)
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sparse M-estimator in semi-parametric copula models2022

    • Author(s)
      Benjamin Poignard
    • Organizer
      Workshop of Copulas
    • Related Report
      2022 Research-status Report
    • Invited

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Published: 2022-04-19   Modified: 2024-12-25  

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