Skip to main content
SpringerLink
Log in

Parametric and Non-parametric Criteria for Causal Inference from Time-Series

  • Chapter
Directed Information Measures in Neuroscience

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Granger causality constitutes a criterion for causal inference from time series that has been largely applied to study causal interactions in the brain from electrophysiological recordings. This criterion underlies the classical parametric implementation in terms of linear autoregressive processes as well as Transfer entropy, i.e. a non-parametric implementation in the framework of information theory. In the spectral domain, partial directed coherence and the Geweke formulation are related to Granger causality but rely on alternative criteria for causal inference which are inherently based on the parametric formulation in terms of autoregressive processes. Here we clearly differentiate between criteria for causal inference and measures used to test them. We compare the different criteria for causal inference from timeseries and we further introduce new criteria that complete a unified picture of how the different approaches are related. Furthermore, we compare the different measures that implement these criteria in the information theory framework.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amblard, P.O., Michel, O.: On directed information theory and Granger causality graphs. J. Comput. Neurosci. 30, 7–16 (2011)

    Article  MathSciNet  Google Scholar 

  2. Ancona, N., Marinazzo, D., Stramaglia, S.: Radial basis function approach to nonlinear Granger causality of time series. Phys. Rev. E 70(5), 056221 (2004)

    Google Scholar 

  3. Andrzejak, R.G., Ledberg, A., Deco, G.: Detection of event-related time-dependent directional couplings. New. J. Phys. 8, 6 (2006)

    Article  Google Scholar 

  4. Ay, N., Polani, D.: Information flows in causal networks. Advances in Complex Systems 11, 17–41 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Baccala, L., Sameshima, K.: Partial directed coherence: a new concept in neural structure determination. Biol. Cybern. 84(1), 463–474 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Baccala, L., Sameshima, K., Ballester, G., Do Valle, A., Timo-Iaria, C.: Studying the interaction between brain structures via directed coherence and Granger causality. Appl. Sig. Process. 5, 40–48 (1999)

    Article  Google Scholar 

  7. 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)

    Article  Google Scholar 

  8. Besserve, M., Schoelkopf, B., Logothetis, N.K., Panzeri, S.: Causal relationships between frequency bands of extracellular signals in visual cortex revealed by an information theoretic analysis. J. Comput. Neurosci. 29(3), 547–566 (2010)

    Article  Google Scholar 

  9. Bressler, S.L., Richter, C.G., Chen, Y., Ding, M.: Cortical functional network organization from autoregressive modeling of local field potential oscillations. Stat. Med. 26(21), 3875–3885 (2007)

    Article  MathSciNet  Google Scholar 

  10. Bressler, S.L., Seth, A.K.: Wiener-Granger causality: A well established methodology. Neuroimage 58(2), 323–329 (2011)

    Article  Google Scholar 

  11. Brovelli, A., Ding, M., Ledberg, A., Chen, Y., Nakamura, R., Bressler, S.L.: Beta oscillations in a large-scale sensorimotor cortical network: Directional influences revealed by Granger causality. P Natl. Acad. Sci. USA 101, 9849–9854 (2004)

    Article  Google Scholar 

  12. Chamberlain, G.: The general equivalence of Granger and Sims causality. Econometrica 50(3), 569–581 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  13. Chen, Y., Bressler, S., Ding, M.: Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data. J. Neurosci. Meth. 150(2), 228–237 (2006)

    Article  MathSciNet  Google Scholar 

  14. Chicharro, D.: On the spectral formulation of Granger causality. Biol. Cybern. 105(5-6), 331–347 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chicharro, D., Ledberg, A.: Framework to study dynamic dependencies in networks of interacting processes. Phys. Rev. E 86, 41901 (2012)

    Article  Google Scholar 

  16. Chicharro, D., Ledberg, A.: When two become one: The limits of causality analysis of brain dynamics. PLoS One 7(3), e32466 (2012)

    Google Scholar 

  17. Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. John Wiley and Sons (2006)

    Google Scholar 

  18. Ding, M., Chen, Y., Bressler, S.L.: Granger causality: Basic theory and application to neuroscience. In: Handbook of Time Series Analysis: Recent Theoretical Developments and Applications, pp. 437–460. Wiley-VCH Verlag (2006)

    Google Scholar 

  19. Eichler, M.: A graphical approach for evaluating effective connectivity in neural systems. Phil. Trans. R Soc. B 360, 953–967 (2005)

    Article  Google Scholar 

  20. Eichler, M.: On the evaluation of information flow in multivariate systems by the directed transfer function. Biol. Cybern. 94(6), 469–482 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  21. Eichler, M.: Granger causality and path diagrams for multivariate time series. J. Econometrics 137, 334–353 (2007)

    Article  MathSciNet  Google Scholar 

  22. Faes, L., Nollo, G., Porta, A.: Information-based detection of nonlinear Granger causality in multivariate processes via a nonuniform embedding technique. Phys. Rev. E 83(5), 051112 (2011)

    Google Scholar 

  23. Friston, K.J.: Functional and effective connectivity: A review. Brain Connectivity 1(1), 13–36 (2012)

    Article  Google Scholar 

  24. Gelfand, I., Yaglom, A.: Calculation of the amount of information about a random function contained in another such function. Am. Math. Soc. Transl. Ser. 2(12), 199–246 (1959)

    MathSciNet  Google Scholar 

  25. Geweke, J.F.: Measurement of linear dependence and feedback between multiple time series. J. Am. Stat. Assoc. 77(378), 304–313 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  26. Geweke, J.F.: Measures of conditional linear dependence and feedback between time series. J. Am. Stat. Assoc. 79(388), 907–915 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  27. Gómez-Herrero, G., Wu, W., Rutanen, K., Soriano, M.C., Pipa, G., Vicente, R.: Assessing coupling dynamics from an ensemble of time series. arXiv:1008.0539v1 (2010)

    Google Scholar 

  28. Gourevitch, B., Le Bouquin-Jeannes, R., Faucon, G.: Linear and nonlinear causality between signals: methods, examples and neurophysiological applications. Biol. Cybern. 95(4), 349–369 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. Granger, C.W.J.: Economic processes involving feedback. Information and Control 6, 28–48 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  30. Granger, C.W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37(3), 424–438 (1969)

    Article  MathSciNet  Google Scholar 

  31. Granger, C.W.J.: Testing for causality: A personal viewpoint. J. Econ. Dynamics and Control 2(1), 329–352 (1980)

    MathSciNet  Google Scholar 

  32. Guo, S., Seth, A.K., Kendrick, K.M., Zhou, C., Feng, J.: Partial Granger causality - eliminating exogenous inputs and latent variables. J. Neurosci. Meth. 172(1), 79–93 (2008)

    Article  Google Scholar 

  33. Hiemstra, C., Jones, J.D.: Testing for linear and nonlinear Granger causality in the stock price-volume relation. J. Financ. 49(5), 1639–1664 (1994)

    Google Scholar 

  34. Hlaváčkova-Schindler, K., Paluš, M., Vejmelka, M., Bhattacharya, J.: Causality detection based on information-theoretic approaches in time-series analysis. Phys. Rep. 441, 1–46 (2007)

    Article  Google Scholar 

  35. Kaminski, M., Blinowska, K.: A new method of the description of the information flow in the brain structures. Biol. Cybern. 65(3), 203–210 (1991)

    Article  MATH  Google Scholar 

  36. Kramers, G.: Directed information for channels with feedback. PhD dissertation, Swiss Federal Institute of Technology, Zurich (1998)

    Google Scholar 

  37. Kuersteiner, G.: Granger-Sims causality, 2nd edn. The New Palgrave Dictionary of Economics (2008)

    Google Scholar 

  38. Kullback, S.: Information Theory and Statistics. Dover, Mineola (1959)

    MATH  Google Scholar 

  39. Lizier, J.T., Prokopenko, M., Zomaya, A.Y.: Local information transfer as a spatiotemporal filter for complex systems. Phys. Rev. E 77, 26110 (2008)

    Article  MathSciNet  Google Scholar 

  40. Lütkepohl, H.: New introduction to multiple time series analysis. Springer, Berlin (2006)

    MATH  Google Scholar 

  41. Marinazzo, D., Pellicoro, M., Stramaglia, S.: Causal information approach to partial conditioning in multivariate data sets. Comput. Math. Meth. Med., 303601 (2012)

    Google Scholar 

  42. Marko, H.: Bidirectional communication theory - generalization of information-theory. IEEE T. Commun. 12, 1345–1351 (1973)

    Article  Google Scholar 

  43. Massey, J.: Causality, feedback and directed information. In: Proc. Intl. Symp. Info. Th. Appli., Waikiki, Hawai, USA (1990)

    Google Scholar 

  44. Paluš, M., Komárek, V., Hrnčíř, Z., Štěrbová, K.: Synchronization as adjustment of information rates: Detection from bivariate time series. Phys. Rev. E 63, 046211 (2001)

    Google Scholar 

  45. Pearl, J.: Causality: Models, Reasoning, Inference, 2nd edn. Cambridge University Press, New York (2009)

    Book  Google Scholar 

  46. Pereda, E., Quian Quiroga, R., Bhattacharya, J.: Nonlinear multivariate analysis of neurophysiological signals. Prog. Neurobiol. 77, 1–37 (2005)

    Article  Google Scholar 

  47. Permuter, H., Kim, Y., Weissman, T.: Interpretations of directed information in portfolio theory, data compression, and hypothesis testing. IEEE Trans. Inf. Theory 57(3), 3248–3259 (2009)

    MathSciNet  Google Scholar 

  48. Priestley, M.: Spectral analysis and time series. Academic Press Inc., San Diego (1981)

    MATH  Google Scholar 

  49. Quinn, C.J., Coleman, T.P., Kiyavash, N., Hatsopoulos, N.G.: Estimating the directed information to infer causal relationships in ensemble neural spike train recordings. J. Comput. Neurosci. 30, 17–44 (2011)

    Article  MathSciNet  Google Scholar 

  50. Roebroeck, A., Formisano, E., Goebel, R.: The identification of interacting networks in the brain using fmri: Model selection, causality and deconvolution. NeuroImage 58(2), 296–302 (2011)

    Article  Google Scholar 

  51. Rozanov, Y.: Stationary random processes. Holden-Day, San Francisco (1967)

    MATH  Google Scholar 

  52. Schelter, B., Timmer, J., Eichler, M.: Assessing the strength of directed influences among neural signals using renormalized partial directed coherence. J. Neurosci. Meth. 179(1), 121–130 (2009)

    Article  Google Scholar 

  53. Schelter, B., Winterhalder, M., Eichler, M., Peifer, M., Hellwig, B., Guschlbauer, B., Lucking, C., Dahlhaus, R., Timmer, J.: Testing for directed influences among neural signals using partial directed coherence. J. Neurosci. Meth. 152(1-2), 210–219 (2006)

    Article  Google Scholar 

  54. Schreiber, T.: Measuring information transfer. Phys. Rev. Lett. 85, 461–464 (2000)

    Article  Google Scholar 

  55. Sims, C.: Money, income, and causality. American Economic Rev. 62(4), 540–552 (1972)

    Google Scholar 

  56. Solo, V.: On causality and mutual information. In: Proceedings of the 47th IEEE Conference on Decision and Control, pp. 4639–4944 (2008)

    Google Scholar 

  57. Takahashi, D.Y., Baccala, L.A., Sameshima, K.: Information theoretic interpretation of frequency domain connectivity measures. Biol. Cybern. 103(6), 463–469 (2010)

    Article  MathSciNet  Google Scholar 

  58. Valdes-Sosa, P., Roebroeck, A., Daunizeau, J., Friston, K.: Effective connectivity: Influence, causality and biophysical modeling. Neuroimage 58(2), 339–361 (2011)

    Article  Google Scholar 

  59. Vicente, R., Wibral, M., Lindner, M., Pipa, G.: Transfer entropy: A model-free measure of effective connectivity for the neurosciences. J. Comput. Neurosci. 30, 45–67 (2010)

    Article  MathSciNet  Google Scholar 

  60. Wiener, N.: The theory of prediction. In: Modern Mathematics for Engineers, pp. 165–190. McGraw-Hill, New York (1956)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Neuroscience and Cognitive Systems UniTn, Istituto Italiano di Tecnologia, Via Bettini 31, 38068, Rovereto, TN, Italy

    Daniel Chicharro

Authors
  1. Daniel Chicharro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Chicharro .

Editor information

Editors and Affiliations

  1. Brain Imaging Center, Frankfurt am Main, Germany

    Michael Wibral

  2. Max-Planck Institute for Brain Research, Frankfurt am Main, Germany

    Raul Vicente

  3. CSIRO Computational Informatics, Marsfield, Sydney, Australia

    Joseph T. Lizier

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Chicharro, D. (2014). Parametric and Non-parametric Criteria for Causal Inference from Time-Series. In: Wibral, M., Vicente, R., Lizier, J. (eds) Directed Information Measures in Neuroscience. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54474-3_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54474-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54473-6

  • Online ISBN: 978-3-642-54474-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation