Double Asymptotics for Explosive Continuous Time Models

Xiaohu Wang () and Jun Yu
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Xiaohu Wang: School of Economics and Sim Kee Boon Institute for Financial Economics, Singapore Management University

No 16-2012, Working Papers from Singapore Management University, School of Economics

Abstract: This paper develops a double asymptotic limit theory for the persistent parameter (k) in explosive continuous time models driven by Lévy processes with a large number of time span (N) and a small number of sampling interval (h). The simultaneous double asymptotic theory is derived using a technique in the same spirit as in Phillips and Magdalinos (2007) for the mildly explosive discrete time model. Both the intercept term and the initial condition appear in the limiting distribution. In the special case of explosive continuous time models driven by the Brownian motion, we develop the limit theory that allows for the joint limits where N ! 1 and h ! 0 simultaneously, the sequential limits where N ! 1 is followed by h ! 0, and the sequential limits where h ! 0 is followed by N ! 1. All three asymptotic distributions are the same.

Keywords: Explosive; Continuous Time; Lévy Process; Invariance Principle; Double Asymptotics (search for similar items in EconPapers)
JEL-codes: C13 C22 G13 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2012-01
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sea
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Published in SMU Economics and Statistics Working Paper Series

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Related works:
Journal Article: Double asymptotics for explosive continuous time models (2016)
Working Paper: Double Asymptotics for an Explosive Continuous Time Model (2011)
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