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Double Asymptotics for Explosive Continuous Time Models

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xiaohu Wang & Jun Yu, 2012. "Double Asymptotics for Explosive Continuous Time Models," Working Papers 16-2012, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:16-2012
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Chen, Ye & Phillips, Peter C.B. & Yu, Jun, 2017. "Inference in continuous systems with mildly explosive regressors," Journal of Econometrics, Elsevier, vol. 201(2), pages 400-416.
    2. Laurent, Sébastien & Shi, Shuping, 2020. "Volatility estimation and jump detection for drift–diffusion processes," Journal of Econometrics, Elsevier, vol. 217(2), pages 259-290.
    3. Cagli, Efe Caglar, 2019. "Explosive behavior in the prices of Bitcoin and altcoins," Finance Research Letters, Elsevier, vol. 29(C), pages 398-403.
    4. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.
    5. Wang, Xiaohu & Xiao, Weilin & Yu, Jun, 2023. "Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process," Journal of Econometrics, Elsevier, vol. 232(2), pages 389-415.
    6. Li, Yicun & Teng, Yuanyang, 2023. "Statistical inference in discretely observed fractional Ornstein–Uhlenbeck processes," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. Yiu Lim Lui & Weilin Xiao & Jun Yu, 2022. "The Grid Bootstrap for Continuous Time Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1390-1402, June.
    8. Katsuto Tanaka & Weilin Xiao & Jun Yu, 2020. "Maximum Likelihood Estimation for the Fractional Vasicek Model," Econometrics, MDPI, vol. 8(3), pages 1-28, August.
    9. Stelios Arvanitis & Tassos Magdalinos, 2018. "Mildly Explosive Autoregression Under Stationary Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 892-908, November.
    10. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic theory for rough fractional Vasicek models," Economics Letters, Elsevier, vol. 177(C), pages 26-29.
    11. Junichi Hirukawa & Sangyeol Lee, 2021. "Asymptotic properties of mildly explosive processes with locally stationary disturbance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 511-534, May.
    12. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2017. "Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour," Economics and Statistics Working Papers 18-2017, Singapore Management University, School of Economics.
    13. 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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    More about this item

    Keywords

    Explosive; Continuous Time; Lévy Process; Invariance Principle; Double Asymptotics;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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