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Limit Laws in Transaction-Level Asset Price Models

Author

Listed:
  • Alexander Aue

    (Department of Statistics - UC Davis - University of California [Davis] - UC - University of California)

  • Lajos Horváth

    (Mathematics department - University of Utah)

  • Clifford M. Hurvich

    (IOMS - Information, Operations and Management Science - NYU - New York University [New York] - NYU - NYU System)

  • Philippe Soulier

    (MODAL'X - Modélisation aléatoire de Paris X - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider pure-jump transaction-level models for asset prices in continuous time, driven by point processes. In a bivariate model that admits cointegration, we allow for time deformations to account for such effects as intraday seasonal patterns in volatility, and non-trading periods that may be different for the two assets. We also allow for asymmetries (leverage effects). We obtain the asymptotic distribution of the log-price process. We also obtain the asymptotic distribution of the ordinary least-squares estimator of the cointegrating parameter based on data sampled from an equally-spaced discretization of calendar time, in the case of weak fractional cointegration. For this same case, we obtain the asymptotic distribution for a tapered estimator under more

Suggested Citation

  • Alexander Aue & Lajos Horváth & Clifford M. Hurvich & Philippe Soulier, 2014. "Limit Laws in Transaction-Level Asset Price Models," Post-Print hal-00583372, HAL.
    • Handle: RePEc:hal:journl:hal-00583372
    DOI: 10.1017/S0266466613000406
    Note: View the original document on HAL open archive server: https://hal.science/hal-00583372v2
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    References listed on IDEAS

    as
    1. Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006. "Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 29-58.
    2. Hurvich, Cliiford & Wang, Yi, 2006. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration, Leverage, and Nonsynchronous Trading Effects," MPRA Paper 1413, University Library of Munich, Germany.
    3. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
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    5. Hurvich, Clifford M. & Wang, Yi, 2010. "A Pure-Jump Transaction-Level Price Model Yielding Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 539-558.
    6. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    7. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
    8. BAUWENS, Luc & VEREDAS, David, 1999. "The stochastic conditional duration model: a latent factor model for the analysis of financial durations," LIDAM Discussion Papers CORE 1999058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
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    Cited by:

    1. Zhang, Yichen & Hurvich, Clifford M., 2022. "Estimation of α, β and portfolio weights in a pure-jump model with long memory in volatility," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 972-994.
    2. Pierre Perron & Eduardo Zorita & Wen Cao & Clifford Hurvich & Philippe Soulier, 2017. "Drift in Transaction-Level Asset Price Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 769-790, September.

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    Keywords

    Point processes; fractional cointegration;

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