Direct Estimation of Lead–Lag Relationships Using Multinomial Dynamic Time Warping

  • Katsuya ItoEmail author
  • Ryuta Sakemoto
Original Research


This paper investigates the lead–lag relationships in high-frequency data. We propose multinomial dynamic time warping (MDTW) that deals with non-synchronous observation, vast data, and time-varying lead–lag. MDTW directly estimates the lead–lags without lag candidates. Its computational complexity is linear with respect to the number of observation and it does not depend on the number of lag candidates. The experiments adopting artificial data and market data illustrate the effectiveness of our method compared to the existing methods.


Lead–lag relationships High frequency trading Dynamic time warping 

JEL Classification

C63 C58 


  1. Brock, W. A., & Kleidon, A. W. (1992). Periodic market closure and trading volume. Journal of Economic Dynamics and Control, 16(3–4), 451–489. Scholar
  2. Chiba, K. (2017). Estimation of the lead-lag parameter between two stochastic processes driven by fractional Brownian motions. arXiv:1705.10466.
  3. Dobreva, D., & Schaumburgb, E. (2017). High-frequency cross-market trading: Model free measurement and applications. Working paper.Google Scholar
  4. Eun, C. S., & Shim, S. (1989). International transmission of stock market movements. The Journal of Financial and Quantitative Analysis, 24(2), 241. Scholar
  5. Garbade, K. D., & Silber, W. L. (1979). Dominant and satellite markets: A study of dually-traded securities. The Review of Economics and Statistics, 61(3), 455. Scholar
  6. Hayashi, T., & Koike, Y. (2017). Multi-scale analysis of lead-lag relationships in high-frequency financial markets. arXiv:1708.03992.
  7. Hayashi, T., & Koike, Y. (2018). Wavelet-based methods for high-frequency lead-lag analysis. SIAM Journal on Financial Mathematics, 9(4), 1208–1248. Scholar
  8. Hayashi, T., & Yoshida, N. (2005). On covariance estimation of non-synchronously observed diffusion processes. Bernoulli, 11(2), 359–379. Scholar
  9. Hendershott, T., & Riordan, R. (2012). High frequency trading and price discovery. SSRN Electronic Journal. Scholar
  10. Hoffmann, M., Rosenbaum, M., & Yoshida, N. (2013). Estimation of the lead-lag parameter from non-synchronous data. Bernoulli, 19(2), 426–461. Scholar
  11. Huth, N., & Abergel, F. (2014). High frequency lead/lag relationships: Empirical facts. Journal of Empirical Finance, 26, 41–58. Scholar
  12. Ito, T., Lyons, R. K., & Melvin, M. T. (1998). Is there private information in the FX market? The Tokyo experiment. The Journal of Finance, 53(3), 1111–1130. Scholar
  13. Kawaller, I. G., Koch, P. D., & Koch, T. W. (1987). The temporal price relationship between s&p 500 futures and the s&p 500 index. The Journal of Finance, 42(5), 1309–1329. Scholar
  14. Lo, A. W., & MacKinlay, A. C. (1990). An econometric analysis of nonsynchronous trading. Journal of Econometrics, 45(1–2), 181–211. Scholar
  15. Lucca, D. O., & Moench, E. (2015). The pre-FOMC announcement drift. The Journal of Finance, 70(1), 329–371. Scholar
  16. Müller, M. (2007). Information retrieval for music and motion. Berlin: Springer. Scholar
  17. Peiers, B. (1997). Informed traders, intervention, and price leadership: A deeper view of the microstructure of the foreign exchange market. The Journal of Finance, 52(4), 1589–1614. Scholar
  18. Raihan, T. (2017). Predicting US recessions: A dynamic time warping exercise in economics. SSRN Electronic Journal,. Scholar
  19. Salvador, S., & Chan, P. (2007). FastDTW: Toward accurate dynamic time warping in linear time and space. Intelligent Data Analysis, 11(5), 561–580. Scholar

Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Graduate School of EconomicsThe University of TokyoBunkyoJapan
  2. 2.YJFX, Inc.TokyoJapan
  3. 3.Keio UniversityChiyodaJapan

Personalised recommendations