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Double Asymptotics for an Explosive Continuous Time Model

Author

Listed:
  • 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.

Suggested Citation

  • Xiaohu Wang & Jun Yu, 2011. "Double Asymptotics for an Explosive Continuous Time Model," Working Papers 16-2011, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:16-2011
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    File URL: https://mercury.smu.edu.sg/rsrchpubupload/19545/doubleasymptotics08.pdf
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    References listed on IDEAS

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    1. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    2. Qiankun Zhou & Jun Yu, 2010. "Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes," Working Papers 20-2010, Singapore Management University, School of Economics.
    3. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    4. 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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    Cited by:

    1. Chambers, MJ, 2016. "The Effects of Sampling Frequency on Detrending Methods for Unit Root Tests," Economics Discussion Papers 16062, University of Essex, Department of Economics.

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