Abstract
Symbolic transfer entropy is a powerful non-parametric tool to detect lead-lag between time series. Because a closed expression of the distribution of Transfer Entropy is not known for finite-size samples, statistical testing is often performed with bootstraps whose slowness prevents the inference of large lead-lag networks between long time series. On the other hand, the asymptotic distribution of Transfer Entropy between two time series is known. In this work, we derive the asymptotic distribution of the test for one time series having a larger Transfer Entropy than another one on a target time series. We then measure the convergence speed of both tests in the small sample size limits via benchmarks. We then introduce Transfer Entropy between time-shifted time series, which allows to measure the timescale at which information transfer is maximal and vanishes. We finally apply these methods to tick-by-tick price changes of several hundreds of stocks, yielding non-trivial statistically validated networks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barnett, L., Barrett, A.B., Seth, A.K.: Granger causality and transfer entropy are equivalent for Gaussian variables. Phys. Rev. Lett. 103(23), 238701 (2009)
Barnett, L., Bossomaier, T.: Transfer entropy as a log-likelihood ratio. Phys. Rev. Lett. 109(13), 138105 (2012)
Bongiorno, C., London, A., Micciche, S., Mantegna, R.N.: Core of communities in bipartite networks. Phys. Rev. E 96(2), 022321 (2017)
Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 424–438 (1969)
Hadash, G., Kermany, E., Carmeli, B., Lavi, O., Kour, G., Jacovi, A.: Estimate and replace: a novel approach to integrating deep neural networks with existing applications. arXiv preprint: arXiv:1804.09028 (2018)
Harré, M.: Entropy and transfer entropy: the Dow Jones and the build up to the 1997 Asian crisis. In: Proceedings of the International Conference on Social Modeling and Simulation, Econophysics Colloquium 2014, pp. 15–25. Springer, Cham (2015)
Kontoyiannis, I., Skoularidou, M.: Estimating the directed information and testing for causality. IEEE Trans. Inf. Theory 62(11), 6053–6067 (2016)
Miller, R.G.: Simultaneous Statistical Inference. Springer (1981)
Newman, M.: Networks: An Introduction, p. 225. Oxford University Press (2010)
Schreiber, T.: Measuring information transfer. Phys. Rev. Lett. 85(2), 461 (2000)
Smirnov, D.A.: Spurious causalities with transfer entropy. Phys. Rev. E 87(4), 042917 (2013)
Staniek, M., Lehnertz, K.: Symbolic transfer entropy. Phys. Rev. Lett. 100(15), 158101 (2008)
Tumminello, M., Micciche, S., Lillo, F., Piilo, J., Mantegna, R.N.: Statistically validated networks in bipartite complex systems. PLoS ONE 6(3), e17994 (2011)
Vuong, Q.H.: Likelihood ratio tests for model selection and non-nested hypotheses. Econ. J. Econ. Soc. 307–333 (1989)
Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9(1), 60–62 (1938)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Bongiorno, C., Challet, D. (2023). Statistical Inference of Lead-Lag Between Asynchronous Time Series from P-Values of Transfer Entropy at Various Timescales. In: Cherifi, H., Mantegna, R.N., Rocha, L.M., Cherifi, C., Miccichè, S. (eds) Complex Networks and Their Applications XI. COMPLEX NETWORKS 2016 2022. Studies in Computational Intelligence, vol 1077. Springer, Cham. https://doi.org/10.1007/978-3-031-21127-0_42
Download citation
DOI: https://doi.org/10.1007/978-3-031-21127-0_42
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-21126-3
Online ISBN: 978-3-031-21127-0
eBook Packages: EngineeringEngineering (R0)