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Malliavin-Mancino estimators implemented with non-uniform fast Fourier transforms

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  • Patrick Chang
  • Etienne Pienaar
  • Tim Gebbie

Abstract

We implement and test kernel averaging Non-Uniform Fast Fourier Transform (NUFFT) methods to enhance the performance of correlation and covariance estimation on asynchronously sampled event-data using the Malliavin-Mancino Fourier estimator. The methods are benchmarked for Dirichlet and Fej\'{e}r Fourier basis kernels. We consider test cases formed from Geometric Brownian motions to replicate synchronous and asynchronous data for benchmarking purposes. We consider three standard averaging kernels to convolve the event-data for synchronisation via over-sampling for use with the Fast Fourier Transform (FFT): the Gaussian kernel, the Kaiser-Bessel kernel, and the exponential of semi-circle kernel. First, this allows us to demonstrate the performance of the estimator with different combinations of basis kernels and averaging kernels. Second, we investigate and compare the impact of the averaging scales explicit in each averaging kernel and its relationship between the time-scale averaging implicit in the Malliavin-Mancino estimator. Third, we demonstrate the relationship between time-scale averaging based on the number of Fourier coefficients used in the estimator to a theoretical model of the Epps effect. We briefly demonstrate the methods on Trade-and-Quote (TAQ) data from the Johannesburg Stock Exchange to make an initial visualisation of the correlation dynamics for various time-scales under market microstructure.

Suggested Citation

  • Patrick Chang & Etienne Pienaar & Tim Gebbie, 2020. "Malliavin-Mancino estimators implemented with non-uniform fast Fourier transforms," Papers 2003.02842, arXiv.org, revised Nov 2020.
    • Handle: RePEc:arx:papers:2003.02842
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    References listed on IDEAS

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    1. Maria Elvira Mancino & Simona Sanfelici, 2011. "Estimating Covariance via Fourier Method in the Presence of Asynchronous Trading and Microstructure Noise," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 367-408, Spring.
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    4. D. Hendricks & T. Gebbie & D. Wilcox, 2016. "Detecting intraday financial market states using temporal clustering," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1657-1678, November.
    5. Michael C. Münnix & Rudi Schäfer & Thomas Guhr, 2011. "Statistical Causes For The Epps Effect In Microstructure Noise," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(08), pages 1231-1246.
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    7. A. Saichev & D. Sornette, 2014. "A simple microstructure return model explaining microstructure noise and Epps effects," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(06), pages 1-36.
    8. Dieter Hendricks & Diane Wilcox, 2014. "A reinforcement learning extension to the Almgren-Chriss model for optimal trade execution," Papers 1403.2229, arXiv.org.
    9. Dieter Hendricks, 2016. "Using real-time cluster configurations of streaming asynchronous features as online state descriptors in financial markets," Papers 1603.06805, arXiv.org, revised May 2017.
    10. Cuchiero, Christa & Teichmann, Josef, 2015. "Fourier transform methods for pathwise covariance estimation in the presence of jumps," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 116-160.
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    12. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, vol. 6(1), pages 49-61.
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    Cited by:

    1. Patrick Chang & Etienne Pienaar & Tim Gebbie, 2020. "Using the Epps effect to detect discrete processes," Papers 2005.10568, arXiv.org, revised Oct 2021.
    2. Chang, Patrick & Pienaar, Etienne & Gebbie, Tim, 2021. "The Epps effect under alternative sampling schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    3. Patrick Chang, 2020. "Fourier instantaneous estimators and the Epps effect," Papers 2007.03453, arXiv.org, revised Sep 2020.
    4. Patrick Chang & Etienne Pienaar & Tim Gebbie, 2020. "The Epps effect under alternative sampling schemes," Papers 2011.11281, arXiv.org, revised Aug 2021.

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