Lévy area analysis and parameter estimation for fOU processes via non-geometric rough path theory

Journal article

This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting. To tackle this problem, we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path. Our approach is particularly suitable for high-frequency data. To formulate the parameter estimators, we introduce a theory of pathwise Itô integrals with respect to fractional Brownian motion. By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes, we demonstrate that our estimators are strongly consistent and pathwise stable. Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings, and may have practical implications for fields including finance, economics, and engineering.

Authors: Qian, Z; Xu, X

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Acta Mathematica Scientia
• Volume: 44
• Issue: 5
• Pages: 1609-1638
• Publication date: 2024-08-27
• Acceptance date: 2024-04-29
• DOI: 10.1007/s10473-024-0501-8
• EISSN: 1572-9087
• ISSN: 0252-9602
• Language: English
• Keywords: pathwise stability; Itô integration; high-frequency data; non-geometric rough path; long time asymptotic; Lévy area; fOU processes