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Double Asymptotics for Explosive Continuous Time Models

  • Xiaohu Wang

    ()

    (School of Economics and Sim Kee Boon Institute for Financial Economics, Singapore Management University)

  • Jun Yu

    ()

    (Sim Kee Boon Institute for Financial Economics, School of Economics and Lee Kong Chian School of Business)

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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.

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Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 16-2012.

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Length: 27 pages
Date of creation: Jan 2012
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:16-2012
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  1. Aue, Alexander & Horv th, Lajos, 2007. "A Limit Theorem For Mildly Explosive Autoregression With Stable Errors," Econometric Theory, Cambridge University Press, vol. 23(02), pages 201-220, April.
  2. Perron, Pierre, 1991. "A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case without an Intercept," Econometrica, Econometric Society, vol. 59(1), pages 211-36, January.
  3. Peter C. B. Phillips & Shu-Ping Shi & Jun Yu, 2013. "Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500," Working Papers 04-2013, Singapore Management University, School of Economics.
  4. 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.
  5. Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA.
  6. Peter C.B. Phillips & Jun Yu, 2007. "Simulation-based Estimation of Contingent-claims Prices," Cowles Foundation Discussion Papers 1596, Cowles Foundation for Research in Economics, Yale University.
  7. Yu, Jun & Phillips, Peter, 2002. "Jacknifing Bond Option Prices," Working Papers 187, Department of Economics, The University of Auckland.
  8. Peter C.B. Phillips & Tassos Magdalinos, 2008. "Unit Root and Cointegrating Limit Theory When Initialization Is in the Infinite Past," Cowles Foundation Discussion Papers 1655, Cowles Foundation for Research in Economics, Yale University.
  9. Shimizu, Yasutaka, 2009. "Notes on drift estimation for certain non-recurrent diffusion processes from sampled data," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2200-2207, October.
  10. Xiaohu Wang & Jun Yu, 2013. "Limit Theory for an Explosive Autoregressive Process," Working Papers 08-2013, Singapore Management University, School of Economics.
  11. Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
  12. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Limit Theory Of Real‐Time Detectors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1079-1134, November.
  13. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  14. Peter C.B. Phillips & Shu-Ping Shi & Jun Yu, 2012. "Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behavior," Cowles Foundation Discussion Papers 1842, Cowles Foundation for Research in Economics, Yale University.
  15. Peter C.B. PHILIPS & Yangru WU & Jun YU, 2009. "Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?," Working Papers 19-2009, Singapore Management University, School of Economics.
  16. Zhou, Qiankun & Yu, Jun, 2015. "Asymptotic theory for linear diffusions under alternative sampling schemes," Economics Letters, Elsevier, vol. 128(C), pages 1-5.
  17. Jun YU, 2009. "Econometric Analysis of Continuous Time Models: A Survey of Peter Phillips' Work and Some New Results," Working Papers 21-2009, Singapore Management University, School of Economics.
  18. Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
  19. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  20. Hu, Yaozhong & Long, Hongwei, 2009. "Least squares estimator for Ornstein-Uhlenbeck processes driven by [alpha]-stable motions," Stochastic Processes and their Applications, Elsevier, vol. 119(8), pages 2465-2480, August.
  21. Magdalinos, Tassos, 2012. "Mildly explosive autoregression under weak and strong dependence," Journal of Econometrics, Elsevier, vol. 169(2), pages 179-187.
  22. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
  23. Tang, Cheng Yong & Chen, Song Xi, 2009. "Parameter estimation and bias correction for diffusion processes," Journal of Econometrics, Elsevier, vol. 149(1), pages 65-81, April.
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