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2023 Fiscal Year Final Research Report

Statistical analysis of high-dimensional high-frequency data

Research Project

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Project/Area Number 19K13668
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 07030:Economic statistics-related
Research InstitutionThe University of Tokyo

Principal Investigator

Koike Yuta  東京大学, 大学院数理科学研究科, 准教授 (80745290)

Project Period (FY) 2019-04-01 – 2024-03-31
Keywords高頻度データ / 高次元共分散推定 / 多重検定 / ファクターモデル
Outline of Final Research Achievements

This study has investigated statistical inference methods for the correlation structure of a large number of financial assets from their high-dimensional high-frequency data. Specifically, I have obtained the following results:
(1) I have proposed a method to estimate the precision matrix of a large number of assets from their high-dimensional high-frequency data. Besides, I have developed a method to approximately compute the distribution of the estimation error. (2) I have developed a theory to systematically estimate the relative errors of normal approximations for various statistics. This serves as justifying the validity of some multiple testing procedures. (3) I have proposed a method to estimate the number of relevant factors from high-frequency data.

Free Research Field

数理統計学、計量ファイナンス

Academic Significance and Societal Importance of the Research Achievements

高次元高頻度データの統計学に関するこれまでの理論的研究は点推定が主流であり、特に推定量の一致性や収束レートに関するものがほとんどであった。すなわち、データ数を多くするにつれて推定誤差が0に近づいていくことは示されてきたが、具体的に推定誤差がどの程度の大きさか見積もる研究はこれまでほとんどなされてこなかった。本研究では、高次元高頻度データの相関構造に対するいくつかの推定量に対して推定誤差の確率分布の近似手法を与え、かつその理論的正当性をある程度一般的な枠組みで示したという点で意義がある。

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Published: 2025-01-30  

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