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Double Asymptotics for an Explosive Continuous Time Model

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  • Xiaohu Wang

    ()
    (School of Economics and Sim Kee Boon Institute for Financial Economics)

  • Jun Yu

    ()
    (School of Economics, Singapore Management Unversity)

Abstract

This paper develops a double asymptotic limit theory for the persistent parameter () 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 ! 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. The initial condition, either xed 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 di¤erent from what was reported in Perron (1991, Econometrica) where the sequential limits, h ! 0 followed by N ! 1, 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.

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File URL: https://mercury.smu.edu.sg/rsrchpubupload/19545/doubleasymptotics08.pdf
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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 16-2011.

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Length: 21 pages
Date of creation: Nov 2011
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:16-2011

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  1. Peter C. B. Phillips & Jun Yu, 2010. "Dating the Timeline of Financial Bubbles during the Subprime Crisis," Cowles Foundation Discussion Papers 1770, Cowles Foundation for Research in Economics, Yale University.
  2. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2007. "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?," Working Papers 222007, Hong Kong Institute for Monetary Research.
  3. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
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