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Asymptotic Theory for Rough Fractional Vasicek Models

Author

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  • Xiao, Weilin

    (Zhejiang University)

  • Yu, Jun

    (School of Economics, Singapore Management University)

Abstract

This paper extends the asymptotic theory for the fractional Vasicek model developed in Xiao and Yu (2018) from the case where H ∈ (1/2, 1) to the case where H ∈ (0, 1/2). It is found that the asymptotic theory of the persistence parameter (k) critically depends on the sign of k. Moreover, if k > 0, the asymptotic distribution for the estimator of k is different when H ∈ (0, 1/2) from that when H ∈ (1/2, 1).

Suggested Citation

  • Xiao, Weilin & Yu, Jun, 2018. "Asymptotic Theory for Rough Fractional Vasicek Models," Economics and Statistics Working Papers 7-2018, Singapore Management University, School of Economics.
    • Handle: RePEc:ris:smuesw:2018_007
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    References listed on IDEAS

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    1. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    2. Alexandra Chronopoulou & Frederi G. Viens, 2012. "Stochastic volatility and option pricing with long-memory in discrete and continuous time," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 635-649, December.
    3. Magdalinos, Tassos, 2012. "Mildly explosive autoregression under weak and strong dependence," Journal of Econometrics, Elsevier, vol. 169(2), pages 179-187.
    4. Stelios Arvanitis & Tassos Magdalinos, 2018. "Mildly explosive autoregression under stationary conditional heteroskedasticity," Working Paper series 18-25, Rimini Centre for Economic Analysis.
    5. 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.
    6. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    7. 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.
    8. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    9. Wang, Xiaohu & Yu, Jun, 2015. "Limit theory for an explosive autoregressive process," Economics Letters, Elsevier, vol. 126(C), pages 176-180.
    10. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    11. Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
    12. Alexandra Chronopoulou & Frederi Viens, 2012. "Estimation and pricing under long-memory stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 379-403, May.
    13. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    14. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    15. F. Comte & L. Coutin & E. Renault, 2012. "Affine fractional stochastic volatility models," Annals of Finance, Springer, vol. 8(2), pages 337-378, May.
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    Cited by:

    1. 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.
    2. Yu, Qian & Bajja, Salwa, 2020. "Volatility estimation of general Gaussian Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 163(C).
    3. Yiu Lim Lui & Weilin Xiao & Jun Yu, 2021. "Mildly Explosive Autoregression with Anti‐persistent Errors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(2), pages 518-539, April.
    4. Katsuto Tanaka, 2020. "Comparison of the LS-based estimators and the MLE for the fractional Ornstein–Uhlenbeck process," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 415-434, July.
    5. Li, Yicun & Teng, Yuanyang, 2023. "Statistical inference in discretely observed fractional Ornstein–Uhlenbeck processes," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    6. Qian Yu, 2021. "Least squares estimator of fractional Ornstein–Uhlenbeck processes with periodic mean for general Hurst parameter," Statistical Papers, Springer, vol. 62(2), pages 795-815, April.

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    More about this item

    Keywords

    Least squares; Roughness; Strong consistency; Asymptotic distribution;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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