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Estimation of α, β and portfolio weights in a pure-jump model with long memory in volatility

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  • Zhang, Yichen
  • Hurvich, Clifford M.

Abstract

We investigate a bivariate pure-jump model of stock prices with long memory in volatility, using a marked log-Gaussian Cox process. We show that, due to the non-synchronicity of transactions, the ordinary least squares estimator of the slope in a contemporaneous regression of returns on returns converges to different targets depending on the sampling frequency. Therefore, we propose a transaction-level estimator that makes full use of data in the complete continuous-time record, and show that the estimator of the slope has slow convergence with rate determined by the memory parameter in volatility.

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  • 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.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:972-994
    DOI: 10.1016/j.spa.2020.09.005
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    References listed on IDEAS

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    2. 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.
    3. 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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    7. Aue, Alexander & Horváth, Lajos & Hurvich, Clifford & Soulier, Philippe, 2014. "Limit Laws In Transaction-Level Asset Price Models," Econometric Theory, Cambridge University Press, vol. 30(3), pages 536-579, June.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Deo, Rohit & Hurvich, Clifford M. & Soulier, Philippe & Wang, Yi, 2009. "Conditions For The Propagation Of Memory Parameter From Durations To Counts And Realized Volatility," Econometric Theory, Cambridge University Press, vol. 25(3), pages 764-792, June.
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