Graphical Modeling of Dynamic Relationships in Multivariate Time Series

Handbook of Time Series Analysis: Recent Theoretical Developments and Applications

Volumn , Issue , 2006, Pages 335-372

  Eichler, Michael ^a  

^a MAASTRICHT UNIVERSITY   (Netherlands)

Author keywords

Applications; Dynamic relationships; Granger causality; Graphical modeling; Graphical representations; Markov interpretation; Multivariate time series; Path diagrams; Statistical inference; Time series analysis

Indexed keywords

EID: 44949096463     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9783527609970.ch14     Document Type: Chapter

References (70)

1. B. Schack, P. Rappelsberger, S. Weiss, and E. Möller. Adaptive phase estimation and its application in EEG analysis of word processing. J. Neurosci. Methods, 93:49-59, 1999.
2. H. Liang, M. Ding, R. Nakamura, and S. L. Bressler. Causal influences in primate cerebral cortex during visual pattern discrimination. NeuroReport, 11:2875-2880, 2000.
3. C. W. J. Granger. Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37: 424-438, 1969.
4. C. Hsiao. Autoregressive modeling and causal ordering of econometric variables. J. Econ. Dyn. Control, 4: 243-259, 1982.
5. S. Wright. Correlation and causation. J. Agric. Res., 20: 557-585, 1921.
6. S.Wright. The method of path coefficients. Ann. Math. Stat., 5: 161-215, 1934.
7. J. Whittaker. Graphical Models in Applied Multivariate Statistics. Wiley, Chichester, 1990.
8. D. R. Cox and N. Wermuth. Multivariate Dependences-Models, Analysis and Interpretation. Chapman and Hall, London, 1996.
9. S. L. Lauritzen. Graphical Models. Oxford University Press, Oxford, 1996.
10. D. Edwards. Introduction to Graphical Modelling. Springer, New York, 2nd edition, 2000.
11. J. Pearl. Fusion, propagation and structuring in belief networks. Artif. Intell., 29: 241-288, 1986.
12. J. Pearl. Probabilistic Inference in Intelligent Systems. Morgan Kaufmann, San Mateo, CA, 1988.
13. J. Pearl. Causal diagrams for empirical research (with discussion). Biometrika, 82:669-710, 1995.
14. J. Pearl. Causality. Cambridge University Press, Cambridge, UK, 2000.
15. P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction, and Search. MIT Press, Cambridge, MA, 2nd edition, 2001. With additional material by David Heckerman, Christopher Meek, Gregory F. Cooper and Thomas Richardson.
16. S. L. Lauritzen. Causal inference from graphical models. In O. E. Barndorff-Nielsen, D. R. Cox, and C. Klüppelberg, editors, Complex Stochastic Systems, pages 63-107. CRC Press, London, 2001.
17. M. Eichler. Graphical Models in Time Series Analysis. PhD thesis, Universität Heidelberg, 1999.
18. M. Eichler. Graphical modelling of time series. Technical report, Universität Heidelberg, 2001.
19. M. Eichler. Granger-causality and path diagrams for multivariate time series. J. Econ., 2006. In press.
20. C. A. Sims. Macroeconomics and reality. Econometrica, 48: 1-4, 1980.
21. H. Y. Toda and P. C. B. Philipps. Vector autoregressions and causality. Econometrica, 61: 1367-1393, 1993.
22. B. Hayo. Money-output Granger causality revisited: an empirical analysis of EU countries. Appl. Econ., 31: 1489-1501, 1999.
23. J. F. Geweke. Measures of conditional linear dependence and feedback between time series. J. Am. Stat. Assoc., 79: 907-915, 1984.
24. P. J. Brockwell and R. A. Davis. Time Series: Theory and Methods. Springer, New York, 2nd edition, 1991.
25. K. Sameshima and L. A. Baccalá. Using partial directed coherence to describe neuronal ensemble interactions. J. Neurosci. Methods, 94: 93-103, 1999.
26. L. A. Baccalá and K. Sameshima. Partial directed coherence: a new concept in neural structure determination. Biol. Cybern., 84: 463-474, 2001.
27. T. Haavelmo. The statistical implications of a system f simultaneous equations. Econometrica, 11: 1-12, 1943.
28. A. S. Goldberger. Structural equation models in the social sciences. Econometrica, 40: 979-1001, 1972.
29. K. A. Bollen. Structural Equations with Latent Variables. Wiley, New York, 1989.
30. C. W. J. Granger. Testing for causality, a personal viewpoint. J. Econ. Dyn. Control, 2:329-352, 1980.
31. J. P. Florens and M. Mouchart. A linear theory for noncausality. Econometrica, 53: 157-175, 1985.
32. Y. Hosoya. On the Granger condition for non-causality. Econometrica, 45: 1735-1736, 1977.
33. D. Tjøstheim. Granger-causality in multiple time series. J. Econ., 17: 157-176, 1981.
34. J. F. Geweke. Measurement of linear dependence and feedback between multiple time series. J. Am. Stat. Assoc., 77: 304-313, 1982.
35. M. Kamiński, M. Ding, W. A. Truccolo, and S. L. Bressler. Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. Biol. Cybern., 85: 145-157, 2001.
36. R. Goebel, A. Roebroeck, D.-S. Kim, and E. Formisano. Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. Magn. Reson. Imaging, 21: 1251-1261, 2003.
37. W. Hesse, E. Möller, M. Arnold, and B. Schack. The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies. J. Neurosci. Methods, 124: 27-44, 2003.
38. A. Brovelli, M. Ding, A. Ledberg, Y. Chen, R. Nakamura, and S. L. Bressler. Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by granger causality. Proc. Natl. Acad. Sci. India A., Phys. Sci. USA, 101: 9849-9854, 2004.
39. M. Eichler. A graphical approach for evaluating effective connectivity in neural systems. Philos. Trans. R. Soc. A, Phys. Sci. B, 360: 953-967, 2005.
40. R. Dahlhaus and M. Eichler. Causality and graphical models in time series analysis. In P. Green, N. Hjort, and S. Richardson, editors, Highly Structured Stochastic Systems. University Press, Oxford, 2003.
41. C. M. Queen and J. Q. Smith. Multiregression dynamic models. J. Roy. Stat. Soc. B, 55: 849-870, 1993.
42. M. Reale and G. Tunnicliffe Wilson. Identification of vector AR models with recursive structural errors using conditional independence graphs. Stat. Methods Appl., 10: 49-65, 2001.
43. P. Spirtes, T. S. Richardson, C. Meek, R. Scheines, and C. Glymour. Using path diagrams as a structural equation modelling tool. Soc. Methods Res., 27: 182-225, 1998.
44. J. T. A. Koster. On the validity of theMarkov interpretation of path diagrams of Gaussian structural equations systems with correlated errors. Scand. J. Stat., 26: 413-431, 1999.
45. T. Richardson. Markov properties for acyclic directed mixed graphs. Scand. J. Stat., 30: 145-157, 2003.
46. D. R. Brillinger. Time Series: Data Analysis and Theory. McGraw-Hill, New York, 1981.
47. K. J. Blinowska, R. Kuś, and M. Kamiński. Granger causality and information flow in multivariate processes. Phys. Rev., E, 70:050902(R), 2004.
48. R. Kuś, M. Kamiński, and K. J. Blinowska. Determination of EEG activity propagation: Pair-wise versus multichannel estimate. IEEE Trans. Biomed. Eng., 51: 1501-1510, 2004.
49. M. Kamiński. Determination of transmission patterns in multichannel data. Philos. Trans. R. Soc. A, Phys. Sci. B, 360: 947-952, 2005.
50. J. Corander and M. Villani. A Bayesian approach to modelling graphical vector autoregressions. J. Time Ser. Anal., 27: 141-156, 2006.
51. M. Eichler. Maximum Likelihood Estimation for Graphical Autoregressions. University of Maastricht, 2006. Preprint.
52. H. Lütkepohl. Introduction to Multiple Time Series Analysis. Springer, New York, 1993.
53. M. Eichler. Graphical Modelling for Multivariate Time Series Using Chain Graphs. University of Maastricht, 2006. Preprint.
54. B. Schelter, M. Winterhalder, M. Eichler, M. Peifer, B. Hellwig, B. Guschlbauer, C. H. Lücking, R. Dahlhaus, and J. Timmer. Testing for directed influences among neural signals using partial directed coherence. J. Neurosci. Methods, 152: 210-219, 2006.
55. M. Drton and T. S. Richardson. Iterative conditional fitting for estimation of a covariance matrix with zeros. Technical report, University of Washington, 2004.
56. H. Akaike. Fitting autoregressive models for prediction. Ann. Inst. Stat. Math., 21: 243-247, 1969.
57. G. Schwarz. Estimation the dimension of a model. Ann. Stat., 6: 461-464, 1978.
58. J. Sandkühler and A. A. Eblen-Zajjur. Identification and characterization of rhythmic nociceptive and non-reciceptive spinal dorsal horn neurons in the rat. Neurosci., 61:991-1006, 1994.
59. M. Eichler, R. Dahlhaus, and J. Sandkühler. Partial correlation analysis for the identification of synaptic connections. Biol. Cybern., 89:289-302, 2003. doi: 10.1007/s00422-003-0400-3.
60. R. Dahlhaus and M. Eichler. Causality and graphicalmodels for multivariate time series and point processes. In H. Hutten and P. Kroesl, editors, IFMBE Proceedings EMBEC 2002, volume 3(2), pages 1430-1431, 2002.
61. J. R. Rosenberg, A. M. Amjad, P. Breeze, D. R. Brillinger, and D. M. Halliday. The Fourier approach to the identification of functional coupling between neuronal spike trains. Prog. Biophysics Mol. Biol., 53: 1-31, 1989.
62. M. J. Kamiński and K. J. Blinowska. A new method of the description of the information flow in the brain structures. Biol. Cybern., 65: 203-210, 1991.
63. M. Eichler. On the evaluation of information flow in multivariate systems by the directed transfer function. Technical report, University of Heidelberg, 2005.
64. A. Korzeniewska, M. Manczak, M. Kaminski, K. Blinowska, and S. Kasicki. Determination of information flow direction between brain structures by a modified Directed Transfer Function method (dDTF). J. Neurosci. Methods, 125: 195-207, 2003.
65. R. Dahlhaus. Graphical interaction models for multivariate time series. Metrika, 51: 157-172, 2000.
66. R. Dahlhaus, M. Eichler, and J. Sandkühler. Identification of synaptic connections in neural ensembles by graphical models. J. Neurosci. Meth., 77: 93-107, 1997.
67. J. Timmer, M. Lauk, B. Köster, B. Hellwig, S. Häußler, B. Guschlbauer, V. Radt, M. Eichler, G. Deuschl, and C. H. Lücking. Cross-spectral analysis of tremor time series. Int. J. Bif. Chaos, 10: 2595-2610, 2000.
68. B. Hellwig, S. Häußler, B. Schelter, M. Lauk, B. Guschlbaur, J. Timmer, and C. H. Lücking. Tremor correlated cortical activity in essential tremor. Lancet, 357: 519-523, 2001.
69. R. I. Goldman, J. M. Stern, J. Engel, and M. S. Cohen. Simultaneous EEG and fMRI of the alpha rhythm. NeuroReport, 13: 2487-2492, 2002.
70. E. Martínez-Montes, P. A. Valdés-Sosa, F. Miwakeichi, R. I. Goldman, and M. S. Cohen. Concurrent EEG/fMRI analysis by multiway partial least squares. NeuroImage, 22: 1023-1034, 2004.