The Factor Tree: A Data-Driven Approach to Regime Switching in High-Dimensions
主讲人：
Yundong Tu（Boya Distinguished Professor, Peking University）
主持老师：
（北大经院）王一鸣、刘蕴霆
参与老师：
（北大经院）王熙、王法、巩爱博
时间：
2025年11月7日（周五）
10:00-11:30
地点（线下）：
北京大学经济学院107会议室
主讲人简介：
涂云东，北京大学博雅特聘教授，联合受聘于光华管理学院商务统计与经济计量系和北京大学统计科学中心。入选“日出东方”北大光华青年人才，北京大学优秀博士学位论文指导教师(2017,2021,2024)，北京大学优秀研究生导师(2024)，教育部“长江学者奖励计划”青年长江学者，国家杰出青年科学基金获得者。先后获武汉大学理学学士学位(2004)和经济学硕士学位(2006)、加州大学经济学博士学位(2012，河滨分校)。环亚太青年计量经济学者(YEAP)会议发起人和主要组织者。50余篇学术论文发表在多个国际国内知名专业杂志。著作教材《时间序列分析》由人民邮电出版社于2022年9月出版。研究领域涵盖时间序列分析、非参数计量方法、大数据分析、金融计量和预测等。
报告摘要：
Threshold factor models are pivotal for capturing rapid regime-switching dynamics in high-dimensional time series, yet existing frameworks relying on a single pre-specified threshold variable often suffer from model misspecification and unreliable inferences. This paper introduces a novel factor tree model that integrates classification and regression tree (CART) principles with high-dimensional factor analysis to address structural instabilities driven by multiple threshold variables. The factor tree is constructed via a recursive sample splitting procedure that maximizes reductions in a loss function derived from the second moments of estimated pseudo linear factors. At each step, the algorithm selects the threshold variable and cutoff value yielding the steepest loss reduction, terminating when a data-driven information criterion signals no further improvement. To mitigate overfitting, an information criterion-based node merging algorithm consolidates leaf nodes with identical factor representations. Theoretical analysis establishes consistency in threshold variable selection, threshold estimation, and factor space recovery, supported by extensive Monte Carlo simulations. An empirical application to U.S. financial data demonstrates the factor tree's effectiveness in capturing regime-dependent dynamics, outperforming traditional single-threshold models in decomposing threshold effects and recovering latent factor structures. This framework offers a robust data-driven approach to modeling complex regime transitions in high-dimensional systems.
