Estimation of Large Dimensional Factor Models with an Unknown Number of Breaks

• Main Authors: MA, Shujie, SU, Liangjun
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2016
• Subjects: Break point; Convergence rate; Factor model; Fused Lasso; Group Lasso; Information criterion; Principal component; Structural change; Super-consistency; Time-varying parameter; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1789; https://ink.library.smu.edu.sg/context/soe_research/article/2788/viewcontent/05_2016.pdf
• Institution: Singapore Management University

In this paper we study the estimation of a large dimensional factor model when the factor loadings exhibit an unknown number of changes over time. We propose a novel three-step procedure to detect the breaks if any and then identify their locations. In the first step, we divide the whole time span into subintervals and fit a conventional factor model on each interval. In the second step, we apply the adaptive fused group Lasso to identify intervals containing a break. In the third step, we devise a grid search method to estimate the location of the break on each identified interval. We show that with probability approaching one our method can identify the correct number of changes and estimate the break locations. Simulation studies indicate superb finite sample performance of our method. We apply our method to investigate Stock and Watson’s (2009) U.S. monthly macroeconomic data set and identify five breaks in the factor loadings, spanning 1959-2006.