New statistical inference for locally stable model and its implementation

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400204
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyushu University
• Principal Investigator: Masuda Hiroki 九州大学, 数理学研究院, 教授 (10380669)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 統計的漸近推測 / 疑似安定過程 / 確率微分方程式

Outline of Final Research Achievements

We have mainly developed a novel quasi-likelihood for estimating stochastic differential equations driven by a locally stable Levy process. The proposed quasi-likelihood theoretically outstrips the conventional Gaussian quasi-likelihood. We have deduced the asymptotic mixed normality of the associated estimator, which does not require any stability condition, such as finite moments and ergodicity, allowing us to construct confidence regions in a unified manner. The results broaden perspective of quasi-likelihood construction based on small-time distributional approximation, hence of theoretical basis for high-frequency dependent data analysis.

Free Research Field

数理統計学，確率過程論