Granger causality and transfer entropy Are equivalent for gaussian variables

Physical Review Letters

Volumn 103, Issue 23, 2009, Pages

  Barnett, Lionel ^a   Barrett, Adam B ^a   Seth, Anil K ^a  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AUTO-REGRESSIVE; DATA-DRIVEN; DEPENDENT PROCESS; DIRECTED INFORMATION; GAUSSIAN VARIABLES; GRANGER CAUSALITY; INFORMATION-THEORETIC APPROACH; TRANSFER ENTROPY; VECTOR AUTOREGRESSIONS; WIDE FIELD;

INFORMATION THEORY; REGRESSION ANALYSIS;

ENTROPY;

EID: 71549116419     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.103.238701     Document Type: Article

References (27)

1. J. Pearl, Causality: Models, Reasoning, and Inference (Cambridge University Press, Cambridge, UK, 1999).
2. N. Wiener, in Modern Mathematics for Engineers, edited by, E. Beckenbach, (McGraw-Hill, New York, 1956).
3. C. Granger, Econometrica 37, 424 (1969). ECMTA7 0098-1699 10.2307/1912791
4. A.K. Seth and G. Edelman, Neural Comput. 19, 910 (2007). NEUCEB 0899-7667 10.1162/neco.2007.19.4.910
5. A.J. Cadotte, T.B. DeMarse, P. He, and M. Ding, PLoS ONE 3, e3355 (2008). 1932-6203 10.1371/journal.pone.0003355
6. M. Ding, Y. Chen, and S. Bressler, in Handbook of Time Series Analysis, edited by, S. Schelter,,, M. Winterhalder,, and, J. Timmer, (Wiley, Wienheim, 2006), pp. 438-460.
7. T. Schreiber, Phys. Rev. Lett. 85, 461 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.461
8. M. Paluš, V. Komárek, Z. Hrnčíř, and K. Štěrbová, Phys. Rev. E PLEEE8 1063-651X 63, 046211 (2001). 10.1103/PhysRevE.63.046211
9. M.G. Kendall and A. Stuart, The Advanced Theory of Statistics, Inference and Relationship Vol. 2 (Griffin, London, 1979).
10. S.S. Wilks, Biometrika 24, 471 (1932). BIOKAX 0006-3444 10.1093/biomet/24.3-4.471
11. J. Davidson, Econometric Theory (Wiley-Blackwell, Oxford, UK, 2000).
12. C.W.J. Granger, Inf. Control IFCNA4 0019-9958 6, 28 (1963). 10.1016/S0019-9958(63)90092-5
13. P. Whittle, J. R. Stat. Soc. Ser. B JSTBAJ 0035-9246 15, 125 (1953).
14. J. Geweke, J. Am. Stat. Assoc. JSTNAL 0162-1459 77, 304 (1982). 10.2307/2287238
15. A. Wald, Trans. Am. Math. Soc. 0002-9947 54, 426 (1943). 10.2307/1990256
16. C. Ladroue, S. Guo, K. Kendrick, and J. Feng, PLoS ONE 4, e6899 (2009). 1932-6203 10.1371/journal.pone.0006899
17. L. Barnett, A.B. Barrett, and A.K. Seth (unpublished).
18. A. Kaiser and T. Schreiber, Physica (Amsterdam) 166D, 43 (2002). PDNPDT 0167-2789 10.1016/S0167-2789(02)00432-3
19. A. Papoulis and S. Pillai, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 2002), 4thed.
20. R.A. Horn and C.R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, UK, 1985).
21. B.W. Silverman, Density Estimation for Statistics and Data Analysis, Monographs on Statistics and Applied Probability Vol. 26 (Chapman & Hall, London, 1986).
22. A. Kraskov, H. Stögbauer, and P. Grassberger, Phys. Rev. E PLEEE8 1539-3755 69, 066138 (2004). 10.1103/PhysRevE.69.066138
23. S. Frenzel and B. Pompe, Phys. Rev. Lett. 99, 204101 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.204101
24. Y. Chen, G. Rangarajan, J. Feng, and M. Ding, Phys. Lett. A 324, 26 (2004). PYLAAG 0375-9601 10.1016/j.physleta.2004.02.032
25. N. Ancona, D. Marinazzo, and S. Stramaglia, Phys. Rev. E PLEEE8 1539-3755 70, 056221 (2004). 10.1103/PhysRevE.70.056221
26. O. Sporns and M. Lungarella, PLoS Comp. Biol. 1553-7358 2, e144 (2006). 10.1371/journal.pcbi.0020144
27. D. Marinazzo, M. Pellicoro, and S. Stramaglia, Phys. Rev. Lett. 100, 144103 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.144103