Double asymptotics for explosive continuous time models
Publication Type
Journal Article
Publication Date
7-2016
Abstract
This paper establishes a double asymptotic theory for explosive continuous time Levy-driven processes and the corresponding exact discrete time models. The double asymptotic theory assumes the sample size diverges because the sampling interval (h) shrinks to zero and the time span (N) diverges. Both the simultaneous and sequential double asymptotic distributions are derived. In contrast to the long-time span asymptotics (N -> infinity with fixed h) where no invariance principle applies, the double asymptotic distribution is derived without assuming Gaussian errors, so an invariance principle applies, as the asymptotic theory for the mildly explosive process developed by Phillips and Magdalinos (2007). Like the in-fill asymptotics (h 0 with fixed N) of Perron (1991), the double asymptotic distribution explicitly depends on the initial condition. The convergence rate of the double asymptotics partially bridges that of the long-time-span asymptotics and that of the in-fill asymptotics. Monte Carlo evidence shows that the double asymptotic distribution works well in practically realistic situations and better approximates the finite sample distribution than the asymptotic distribution that is independent of the initial condition. Empirical applications to real Nasdaq prices highlight the difference between the new theory and the theory without taking the initial condition into account. (C) 2016 Elsevier B.V. All rights reserved.
Keywords
Explosive continuous time models;Levy process;Moderate deviations from unity;Double asymptotics;Invariance principle;Initial condition
Discipline
Econometrics
Research Areas
Econometrics
Publication
Journal of Econometrics
Volume
193
Issue
1
First Page
35
Last Page
53
ISSN
0304-4076
Identifier
10.1016/j.jeconom.2016.02.014
Publisher
Elsevier
Citation
WANG, Xiaohu and Jun YU.
Double asymptotics for explosive continuous time models. (2016). Journal of Econometrics. 193, (1), 35-53.
Available at: https://ink.library.smu.edu.sg/soe_research/1858
Additional URL
https://doi.org/10.1016/j.jeconom.2016.02.014