New Distribution Theory for the Estimation of Structural Break Point in Mean

Prof. Yu Jun and Dr. Jiang Liang

Singapore Management University

About the Speaker

Speaker 1:

Professor Yu Jun joined SMU in 2004. Prior to SMU, he was teaching at the University of Auckland. His main research interests are in financial econometrics, empirical asset pricing, and econometric theory. He is a recipient of several awards, including the excellent research award at the University of Auckland, the Lee Kuan Yew fellow for research excellence award (twice) at SMU, and the AR Bergstrom Prize in Econometrics. He was the director of the Sim Kee Boon Institute for Financial Economics at SMU from 2011 to 2013.

Speaker 2:

Dr. Liang Jiang received his Ph.D. in Economics in 2016 from Singapore Management University. He is currently a post-doctoral research fellow in the School of Economics at Singapore Management University. His research interests are in the area of financial econometrics and housing market.

Abstract

Based on the Girsanov theorem, this paper first obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model. The exact distribution is asymmetric and tri-modal, indicating that the estimator is seriously biased. These two properties are also found in the finite sample distribution of the least squares estimator of structural break point in the discrete time model. The paper then builds a continuous time approximation to the discrete time model and develops an in-fill asymptotic theory for the least squares estimator. The obtained in-fill asymptotic distribution is asymmetric and tri-modal and delivers good approximations to the finite sample distribution. In order to reduce the bias in the estimation of both the continuous time model and the discrete time model, a simulation-based method based on the indirect estimation approach is proposed. Monte Carlo studies show that the indirect estimation method achieves substantial bias reductions. However, since the binding function has a slope less than one, the variance of the indirect estimator is larger than that of the original estimator.