Multivariate time series analysis

Understanding Complex Systems

Volumn 2008, Issue , 2008, Pages 1-40

  Schelter, Björn ^a   Dahlhaus, Rainer ^b   Leistritz, Lutz ^c   Hesse, Wolfram ^c   Schack, Bärbel ^c   Kurths, Jürgen ^d   Timmer, Jens ^a   Witte, Herbert ^c  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF HEIDELBERG   (Germany)

^c FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^d UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 37649005158     PISSN: 18600832     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-75632-3_1     Document Type: Article

References (73)

1. C. Allefeld and J. Kurths. An approach to multivariate phase synchronization analysis and its application to event-related potentials. Int. J. Bif. Chaos, 14:417-426, 2004.
2. L. A. Baccala and K. Sameshima. Partial directed coherence: A new concept in neural structure determination. Biol. Cybern., 84:463-474, 2001.
3. A. Bandrivskyy, A. Bernjak, P. V. E. McClintock, and A. Stefanovska. Wavelet phase coherence analysis: Application to skin temperature and blood flow. Cardiovasc. Eng., 4:89-93, 2004.
4. M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld. Huygens's clocks. Proc. R. Soc. Lond. A, 458:563-579, 2002.
5. P. Bloomfield. Fourier Analysis of Time Series: An Introduction. Wiley, New York, 1976.
6. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou. The synchronization of chaotic systems. Phys. Rep., 366:1-101, 2002.
7. S. Boccaletti and D. L. Valladares. Characterization of intermittent lag synchronization. Phys. Rev. E, 62:7497-7500, 2000.
8. D. R. Brillinger. Time Series: Data Analysis and Theory. Holden-Day, Inc., San Francisco, 1981.
9. D. R. Brillinger. Remarks concerning graphical models for time series and point processes. Rev. Econometrica, 16:1-23, 1996.
10. R. Dahlhaus. Graphical interaction models for multivariate time series. Metrika, 51:157-172, 2000.
11. R. Dahlhaus and M. Eichler. Causality and graphical models for time series. In P. Green, N. Hjort, and S. Richardson, editors, Highly Structured Stochastic Systems. Oxford University Press, Oxford, 2003.
12. R. Dahlhaus, M. Eichler, and J. Sandkühler. Identification of synaptic connections in neural ensembles by graphical models. J. Neurosci. Methods, 77:93-107, 1997.
13. M. Eichler. A graphical approach for evaluating effective connectivity in neural systems. Phil. Trans. Royal Soc. B, 360:953-967, 2005.
14. M. Eichler. Granger-causality and path diagrams for multivariate time series. J. Econom., 137:334-353, 2007.
15. M. Eichler. Graphical modeling of dynamic relationships in multivariate time series. In B. Schelter, M. Winterhalder, and J. Timmer, editors, Handbook of Time Series Analysis. Wiley, New York, 2006.
16. M. Eichler, R. Dahlhaus, and J. Sandkühler. Partial correlation analysis for the identification of synaptic connections. Biol. Cybern., 89:289-302, 2003.
17. J. Granger. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 37:424-438, 1969.
18. P. Grosse, M. J. Cassidy, and P. Brown. EEG-EMG, MEG-EMG and EMG-EMG frequency analysis: Physiological principals and clinical applications. Clin. Neurophysiol., 113:1523-1531, 2002.
19. A. C. Harvey. Forecasting Structural Time Series Models and the Kalman Filter. Cambridge University Press, Cambridge, 1994.
20. B. Hellwig, S. Häußler, M. Lauk, B. Köster, B. Guschlbauer, R. Kristeva-Feige, J. Timmer, and C. H. Lücking. Tremor-correlated cortical activity detected by electroencephalography. Electroencephalogr. Clin. Neurophysiol., 111:806-809, 2000.
21. B. Hellwig, S. Häußler, B. Schelter, M. Lauk, B. Guschlbauer, J. Timmer, and C. H. Lücking. Tremor correlated cortical activity in essential tremor. Lancet, 357:519-523, 2001.
22. B. Hellwig, B. Schelter, B. Guschlbauer, J. Timmer, and C. H. Lücking. Dynamic synchronisation of central oscillators in essential tremor. Clin. Neurophysiol., 114:1462-1467, 2003.
23. D. Hemmelmann, W. Hesse, L. Leistritz, T. Wüstenberg, J. Reichenbach, and H. Witte. Example of a 4-dimensional image analysis: Time-variant model-related analysis of fast-fmri sequences. In The 9th Korea-Germany Joint Workshop on Advanced Medical Images Processing, pages 22-28, Seoul, 2006.
24. 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.
25. J. A. Hobson and E. F. Pace-Schott. The cognitive neuroscience of sleep: neuronal systems, consciousness and learning. Nat. Rev. Neurosci., 3:679-693, 2002.
26. N. L. Johnson, S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions. Wiley, New York, 1995.
27. E. G. Jones. Thalamic circuitry and thalamocortical synchrony. Philos. Trans. R. Soc. Lond. B. Biol. Sci., 357:1659-1673, 2002.
28. 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.
29. J. Kent and T. Hainsworth. Confidence intervals for the noncentral chi-squared distribution. J. Stat. Plan. Infer., 46:147-159, 1995.
30. L. Kocarev and U. Parlitz. Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys. Rev. Lett., 76:1816-1819, 1996.
31. R. Kus, M. Kamiński, and K. J. Blinowska. Determination of EEG activity propagation: Pair-wise versus multichannel estimate. IEEE Trans. Biomed. Eng., 51:1501-1510, 2004.
32. L. Leistritz, W. Hesse, M. Arnold, and H. Witte. Development of interaction measures based on adaptive non-linear time series analysis of biomedical signals. Biomed. Tech., 51(2):64-69, 2006. 0013-5585 (Print) Journal Article Research Support, Non-U.S. Gov't.
33. L. Leistritz, W. Hesse, T. Wüstenberg, C. Fitzek, J. R. Reichenbach, and H. Witte. Time-variant analysis of fast-fmri and dynamic contrast agent mri sequences as examples of 4-dimensional image analysis. Meth. Inf. Med., 45(6):643-650, 2006.
34. K. Mardia and P. Jupp. Directional Statistics. Wiley, West Sussex, 2000.
35. E. Möller, B. Schack, M. Arnold, and H. Witte. Instantaneous multivariate EEG coherence analysis by means of adaptive high-dimensional autoregressive models. J. Neurosci. Methods, 105:143-158, 2001.
36. F. Mormann, K. Lehnertz, P. David, and C. E. Elger. Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients. Physica D, 144:358-369, 2000.
37. E. Niedermeyer, D. L. Sherman, R. J. Geocadin, H. C. Hansen, and D. F. Hanley. The burst-suppression electroencephalogram. Clin. Electroencephalogr., 30:99-105, 1999.
38. G. V. Osipov, A. S. Pikovsky, M. G. Rosenblum, and J. Kurths. Phase synchronization effects in a lattice of nonidentical Roessler oscillators. Phys. Rev. E, 55:2353-2361, 1997.
39. G.V. Osipov, J. Kurths, and C. Zhou. Synchronization in Oscillatory Networks. Complexity. Springer, Berlin, 2007.
40. E. F. Pace-Schott and J. A. Hobson. The neurobiology of sleep: Genetics, cellular physiology and subcortical networks. Nat. Rev. Neurosci., 3:591-605, 2002.
41. L. M. Pecora and T. L. Carroll. Synchronization in chaotic systems. Phys. Rev. Lett., 64:821-824, 1990.
42. A. Pikovsky, M. Rosenblum, and J. Kurths. Phase synchronization in regular and chaotic systems. Int. J. Bif. Chaos, 10:2291-2305, 2000.
43. A. Pikovsky, M. Rosenblum, and J. Kurths. Synchronization - A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge, 2001.
44. M. Le Van Quyen, J. Foucher, J. Lachaux, E. Rodriguez, A. Lutz, J. Martinerie, and F. J. Varela. Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony. J. Neurosci. Methods, 111:83-98, 2001.
45. M. G. Rosenblum, A. Pikovsky, J. Kurths, C. Schäfer, and P. A. Tass. Phase synchronization: From theory to data analysis. In F. Moss and S. Gielen, editors, Handbook of Biological Physics, volume 4 of Neuroinformatics, pages 279-321, Elsevier, Amsterdam, 2001.
46. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths. Phase synchronization of chaotic oscillators. Phys. Rev. Lett., 76:1804-1807, 1996.
47. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths. From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett., 78: 4193-4196, 1997.
48. N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and H. D. I. Abarbanel. Generalized synchronization of chaos in directionally coupled chaotic systems. Phys. Rev. E, 51:980-994, 1995.
49. K. Sameshima and L. A. Baccala. Using partial directed coherence to describe neuronal ensemble interactions. J. Neurosci. Methods, 94:93-103, 1999.
50. B. Schack, G. Grießbach, M. Arnold, and J. Bolten. Dynamic cross spectral analysis of biological signals by means of bivariate ARMA processes with time-dependent coefficients. Med. Biol. Eng. Comput. 33:605-610, 1995.
51. 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.
52. B. Schack, S. Weiss, and P. Rappelsberger. Cerebral information transfer during word processing: Where and when does it occur and how fast is it? Hum. Brain Mapp., 19:18-36, 2003.
53. B. Schelter, B. Hellwig, B. Guschlbauer, C. H. Lücking, and J. Timmer. Application of graphical models in bilateral essential tremor. Proc. IFMBE (EMBEC), 2:1442-1443, 2002.
54. B. Schelter, J. Timmer, and M. Eichler. Assessing the strength of directed influences among neural signals using renormalized partial directed coherence, submitted 2007.
55. B. Schelter, M. Winterhalder, R. Dahlhaus, J. Kurths, and J. Timmer. Partial phase synchronization for multivariate synchronizing system. Phys. Rev. Lett., 96:208103, 2006.
56. 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.
57. B. Schelter, M. Winterhalder, B. Hellwig, B. Guschlbauer, C. H. Lücking, and J. Timmer. Direct or indirect? Graphical models for neural oscillators. J. Physiol. Paris, 99:37-46, 2006.
58. B. Schelter, M. Winterhalder, J. Kurths, and J. Timmer. Phase synchronization and coherence analysis: Sensitivity and specificity. Int. J. Bif. Chaos, in press, 2006.
59. B. Schelter, M. Winterhalder, and J. Timmer, editors. Handbook of Time Series Analysis. Wiley-VCH, Berlin, 2006.
60. S. J. Schiff, P. So, T. Chang, R. E. Burke, and T. Sauer. Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. Phys. Rev. E, 54:6708-6724, 1996.
61. S. M. Schnider, R. H. Kwong, F. A. Lenz, and H. C. Kwan. Detection of feedback in the central nervous system using system identification techniques. Biol. Cybern., 60:203-212, 1989.
62. R. H. Shumway and D. S. Stoffer. Time Series Analysis and Its Application. Springer, New York, 2000.
63. M. Steriade. Impact of network activities on neuronal properties in corticothalamic systems. J. Neurophysiol., 86:1-39, 2001.
64. M. Steriade and I. Timofeev. Neuronal plasticity in thalamocortical networks during sleep and waking oscillations. Neuron, 37:563-576, 2003.
65. P. A. Tass, M. G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, and H. J. Freund. Detection of n : M phase locking from noisy data: Application to magnetoencephalography. Phys. Rev. Lett., 81:3291-3295, 1998.
66. J. Timmer, M. Lauk, S. Häußler, V. Radt, B. Köster, B. Hellwig, B. Guschlbauer, C.H. Lücking, M. Eichler, and G. Deuschl. Cross-spectral analysis of tremor time series. Int. J. Bif. Chaos, 10:2595-2610, 2000.
67. J. Timmer, M. Lauk, W. Pfleger, and G. Deuschl. Cross-spectral analysis of physiological tremor and muscle activity. I. Theory and application to unsynchronized EMG. Biol. Cybern., 78:349-357, 1998.
68. J. Volkmann, M. Joliot, A. Mogilner, A. A. Ioannides, F. Lado, E. Fazzini, U. Ribary, and R. Llinás. Central motor loop oscillations in Parkinsonian resting tremor revealed by magnetoencephalography. Neurology, 46:1359-1370, 1996.
69. H. Voss, J. Timmer, and J. Kurths. Nonlinear dynamical system indentification from uncertain and indirect measurements. Int. J. Bif. Chaos, 14:1905-1933, 2004.
70. M. Winterhalder, B. Schelter, W. Hesse, K. Schwab, L. Leistritz, D. Klan, R. Bauer, J. Timmer, and H. Witte. Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems. Sig. Proc., 85:2137-2160, 2005.
71. M. Winterhalder, B. Schelter, W. Hesse, K. Schwab, L. Leistritz, D. Klan, J. Timmer, and H. Witte. Detection of directed information flow in multidimensional biosignals. Special Issue on Biosignal Processing, Biomed. Tech., 51:281-287, 2006.
72. M. Winterhalder, B. Schelter, J. Kurths, A. Schulze-Bonhage, and J. Timmer. Sensitivity and specificity of coherence and phase synchronization analysis. Phys. Lett. A, 356:26-34, 2006.
73. H. Witte, C. Schelenz, M. Specht, H. Jäger, P. Putsche, M. Arnold, L. Leistritz, and K. Reinhart. Interrelations between EEG frequency components in sedated intensive care patients during burst-suppression period. Neurosci. Lett., 260:53-56, 1999.