A Robust Approach to ARMA Factor Modeling

• 成果类型: Article
• 署名作者: Falconi, Lucia; Ferrante, Augusto; Zorzi, Mattia
• 署名单位: University of Padua
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3274710
• 发表日期: 2024
• 页码: 828-841
• 关键词: Convex optimization; duality theory; dynamic factor analysis (DFA); nuclear norm

摘要

This article deals with the dynamic factor analysis problem for an ARMA process. To robustly estimate the number of factors, we construct a confidence region centered in a finite sample estimate of the underlying model, which contains the true model with a prescribed probability. In this confidence region, the problem, formulated as a rank minimization of a suitable spectral density, is efficiently approximated via a trace norm convex relaxation. The latter is addressed by resorting to the Lagrange duality theory, which allows to prove the existence of solutions. Finally, a numerical algorithm to solve the dual problem is presented. The effectiveness of the proposed estimator is assessed through simulation studies both with synthetic and real data.