Publication Type

Journal Article

Version

publishedVersion

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

Additional URL

https://doi.org/10.1016/j.jeconom.2016.02.014

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