Publication Type

Working Paper

Version

publishedVersion

Publication Date

11-2011

Abstract

This paper develops a double asymptotic limit theory for the persistent parameter (θ) in an explosive continuous time model with a large number of time span (N) and a small number of sampling interval (h). The limit theory allows for the joint limits where N → ∞ and h → 0 simultaneously, the sequential limits where N → ∞ is followed by h → 0, and the sequential limits where h → 0 is followed by N → ∞. All three asymptotic distributions are the same. The initial condition, either fixed or random, appears in the limiting distribution. The simultaneous double asymptotic theory is derived by using results recently obtained in Phillips and Magdalinos (2007) for the mildly explosive discrete time model and so a invariance principle applies. However, our asymptotic distribution is different from what was reported in Perron (1991, Econometrica) where the sequential limits, h → 0 followed by N → ∞, were considered. It is shown that the limit theory in Perron is not correct and the correct sequential asymptotic distribution is identical to the simultaneous double asymptotic distribution.

Discipline

Econometrics

Research Areas

Econometrics

First Page

1

Last Page

20

Publisher

SMU Economics and Statistics Working Paper Series, No. 16-2011

City or Country

Singapore

Copyright Owner and License

Authors

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