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Optimal Cross-Correlation Estimates from Asynchronous Tick-by-Tick Trading Data

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  • William H. Press

Abstract

Given two time series, A and B, sampled asynchronously at different times {t_A_i} and {t_B_j}, termed "ticks", how can one best estimate the correlation coefficient \rho between changes in A and B? We derive a natural, minimum-variance estimator that does not use any interpolation or binning, then derive from it a fast (linear time) estimator that is demonstrably nearly as good. This "fast tickwise estimator" is compared in simulation to the usual method of interpolating changes to a regular grid. Even when the grid spacing is optimized for the particular parameters (not often possible in practice), the fast tickwise estimator has generally smaller estimation errors, often by a large factor. These results are directly applicable to tick-by-tick price data of financial assets.

Suggested Citation

  • William H. Press, 2023. "Optimal Cross-Correlation Estimates from Asynchronous Tick-by-Tick Trading Data," Papers 2303.16153, arXiv.org.
    • Handle: RePEc:arx:papers:2303.16153
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    References listed on IDEAS

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    1. de Jong, Frank & Nijman, Theo, 1997. "High frequency analysis of lead-lag relationships between financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 259-277, June.
    2. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    3. Fulvio Corsi & Francesco Audrino, 2007. "Realized Correlation Tick-by-Tick," University of St. Gallen Department of Economics working paper series 2007 2007-02, Department of Economics, University of St. Gallen.
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    1. William H. Press, 2023. "NYSE Price Correlations Are Abitrageable Over Hours and Predictable Over Years," Papers 2305.08241, arXiv.org.

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