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Wavelet-based methods for high-frequency lead-lag analysis

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  • Takaki Hayashi
  • Yuta Koike

Abstract

We propose a novel framework to investigate lead-lag relationships between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice.

Suggested Citation

  • Takaki Hayashi & Yuta Koike, 2016. "Wavelet-based methods for high-frequency lead-lag analysis," Papers 1612.01232, arXiv.org, revised Nov 2018.
    • Handle: RePEc:arx:papers:1612.01232
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    References listed on IDEAS

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    1. Christian M. Hafner, 2012. "Cross-correlating wavelet coefficients with applications to high-frequency financial time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1363-1379, December.
    2. Yuri Kabanov & Robert Liptser, 2006. "From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift," Post-Print hal-00488295, HAL.
    3. Bacry, E. & Delattre, S. & Hoffmann, M. & Muzy, J.F., 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2475-2499.
    4. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
    5. Michael H. Breitner & Christian Dunis & Hans-Jörg Mettenheim & Christopher Neely & Georgios Sermpinis & Hamad Alsayed & Frank McGroarty, 2014. "Ultra‐High‐Frequency Algorithmic Arbitrage Across International Index Futures," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(6), pages 391-408, September.
    6. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    7. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    8. Robert, Christian Y. & Rosenbaum, Mathieu, 2010. "On the limiting spectral distribution of the covariance matrices of time-lagged processes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2434-2451, November.
    9. Gallegati, Marco, 2008. "Wavelet analysis of stock returns and aggregate economic activity," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3061-3074, February.
    10. 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.
    11. Lo, Andrew W. & Craig MacKinlay, A., 1990. "An econometric analysis of nonsynchronous trading," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 181-211.
    12. Kawaller, Ira G & Koch, Paul D & Koch, Timothy W, 1987. "The Temporal Price Relationship between S&P 500 Futures and the S and P 500 Index," Journal of Finance, American Finance Association, vol. 42(5), pages 1309-1329, December.
    13. Nijman, T.E. & de Jong, F.C.J.M., 1997. "High frequency analysis of lead-lag relationships between financial markets," Other publications TiSEM f4f406a0-771a-4af2-9364-6, Tilburg University, School of Economics and Management.
    14. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    15. Medvegyev, Peter, 2007. "Stochastic Integration Theory," OUP Catalogue, Oxford University Press, number 9780199215256.
    16. Duffie, Darrell, 1991. "The theory of value in security markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 31, pages 1615-1682, Elsevier.
    17. Stoll, Hans R. & Whaley, Robert E., 1990. "The Dynamics of Stock Index and Stock Index Futures Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 441-468, December.
    18. W. Hildenbrand & H. Sonnenschein (ed.), 1991. "Handbook of Mathematical Economics," Handbook of Mathematical Economics, Elsevier, edition 1, volume 4, number 4.
    19. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Post-Print hal-01313994, HAL.
    20. Alessandro Cardinali, 2009. "A Generalized Multiscale Analysis Of The Predictive Content Of Eurodollar Implied Volatilities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 1-18.
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    Cited by:

    1. Hayashi, Takaki & Koike, Yuta, 2019. "No arbitrage and lead–lag relationships," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    2. Poutré, Cédric & Dionne, Georges & Yergeau, Gabriel, 2024. "The profitability of lead–lag arbitrage at high frequency," International Journal of Forecasting, Elsevier, vol. 40(3), pages 1002-1021.
    3. Weibing Huang & Mathieu Rosenbaum & Pamela Saliba, 2019. "From Glosten-Milgrom to the whole limit order book and applications to financial regulation," Papers 1902.10743, arXiv.org.
    4. Katsuya Ito & Ryuta Sakemoto, 2020. "Direct Estimation of Lead–Lag Relationships Using Multinomial Dynamic Time Warping," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 27(3), pages 325-342, September.

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