Econometric analysis of continuous time models has drawn the attention of Peter Phillips for 40 years, resulting in many important publications by him. In these publications he has dealt with a wide range of continuous time models and the associated econometric problems. He has investigated problems from univariate equations to systems of equations, from asymptotic theory to finite sample issues, from parametric models to nonparametric models, from identification problems to estimation and inference problems, and from stationary models to nonstationary and nearly nonstationary models. This paper provides an overview of Peter Phillips’ contributions in the continuous time econometrics literature. We review the problems that have been tackled by him, outline the main techniques suggested by him, and discuss the main results obtained by him. Based on his early work, we compare the performance of three asymptotic distributions in a simple setup. Results indicate that the in-fill asymptotics significantly outperforms the long-span asymptotics and the double asymptotics.
Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business, Singapore Management University, 90 Stamford Road, Singapore 178903; email: [email protected].
I gratefully acknowledge financial support from the Ministry of Education AcRF Tier 2 fund under Grant No. MOE2011-T2-2-096. I would like to thank Peter Phillips for extensive discussions on the subject, seminar participants at NZESG and Singapore Management University, Federico Bandi, Bruce Hansen, Xiaohu Wang, Qiankun Zhou, and especially a referee for helpful comments.