Development and implementation of generic statistical methods for non-Gaussian stochastic differential equation models.

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K20230
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60030:Statistical science-related
• Research Institution: Kansai University (2020-2023); The Institute of Statistical Mathematics (2019)
• Principal Investigator: Uehara Yuma 関西大学, システム理工学部, 准教授 (00822545)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 高頻度データ / 統計学 / 確率微分方程式

Outline of Final Research Achievements

We have conducted research on non-Gaussian stochastic differential equation models, which are one of the candidate models for describing high-frequency data. We focus on the construction of statistical methods which can be applied to a wide range of driving noise classes in a unified manner. Specifically, we developed a block bootstrap method to approximate the asymptotic distribution of the Gaussian quasi maximum likelihood estimator, taking into account the model misspecification. We also derived a BIC-type model selection criterion based on the expansion of the log marginal Gaussian quasi likelihood and clarified its properties.

Free Research Field

統計学

Academic Significance and Societal Importance of the Research Achievements

非正規確率微分方程式モデルは, 駆動ノイズの分布特性の豊富さから高い表現力を持っているものの, その微小時間挙動の複雑さが問題となっていた. 本研究により, 広範の非正規確率微分方程式モデルのクラスへ適用可能な統計手法が得られたことで, 高頻度データ解析の発展に寄与すると考えられる.