Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion

• Main Authors: YU, Ping, PHILLIPS, Peter C. B.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Threshold regression; Sequential asymptotics; Doob's martingale inequality; Compound Poisson process; Brownian motion; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2353; https://ink.library.smu.edu.sg/context/soe_research/article/3352/viewcontent/2Asys_av.pdf; https://ink.library.smu.edu.sg/context/soe_research/article/3352/filename/0/type/additional/viewcontent/2Asys_mmc1.pdf
• Institution: Singapore Management University

The asymptotic distribution of the least squares estimator in threshold regression is expressed in terms of a compound Poisson process when the threshold effect is fixed and as a functional of two-sided Brownian motion when the threshold effect shrinks to zero. This paper explains the relationship b...