FACTOR-DRIVEN TWO-REGIME REGRESSION

• 成果类型: Article
• 署名作者: Lee, Sokbae; Liao, Yuan; Seo, Myung Hwan; Shin, Youngki
• 署名单位: Columbia University; Rutgers University System; Rutgers University New Brunswick; Seoul National University (SNU); McMaster University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS2017
• 发表日期: 2021
• 页码: 1656-1678
• 关键词: factor-augmented regression; least-squares estimator; factor models; change-point; inference

摘要

We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold effect shrinks to zero. In particular, we establish a phase transition that describes the effect of first-stage factor estimation as the cross-sectional dimension of panel data increases relative to the time-series dimension. Moreover, we develop bootstrap inference and illustrate our methods via numerical studies.