zbMATH — the first resource for mathematics

On the evaluation of information flow in multivariate systems by the directed transfer function. (English) Zbl 1138.62048
Summary: The directed transfer function (DTF) has been proposed as a measure of information flow between the components of multivariate time series. We discuss the interpretation of the DTF and compare it with other measures for directed relationships. We show that the DTF does not indicate multivariate or bivariate Granger causality, but that it is closely related to the concept of impulse response function and can be viewed as a spectral measure for the total causal influence from one component to another. Furthermore, we investigate the statistical properties of the DTF and establish a simple significance level for testing for the null hypothesis of no information flow.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
92B05 General biology and biomathematics
62P10 Applications of statistics to biology and medical sciences; meta analysis
90B18 Communication networks in operations research
Full Text: DOI
[1] Achermann P, Hartmann R, Gunzinger A, Guggenbühl W, Borbély AA (1994) All night sleep and artificial stochastic control have similar correlation dimension. Electroencephalogr Clin Neurophysiol 90:384–387 · doi:10.1016/0013-4694(94)90054-X
[2] Baccalá LA, Sameshima K (2001) Partial directed coherence: a new concept in neural structure determination. Biol Cybern 84:463–474 · Zbl 1160.92306 · doi:10.1007/PL00007990
[3] Blinowska KJ, Kuś R, Kamiński M (2004). Granger causality and information flow in multivariate processes. Phys Rev E 70:050902(R) · doi:10.1103/PhysRevE.70.050902
[4] Blinowska KJ, Malinowski M (1991) Non-linear and linear forecasting of the EEG time series. Biol Cybern 66:159–165 · doi:10.1007/BF00243291
[5] Brockwell PJ, Davis RA (1991) Time series: theory and methods 2nd edn. Springer Berlin Heidelberg, New York
[6] Brovelli A, Ding MAL, Chen Y, Nakamura R, Bressler SL (2004) Beta oscillations in a large-scale sensorimotor cortical network: directional influences revealed by granger causality. Proc Nat Acad Sci USA 101:9849–9854 · doi:10.1073/pnas.0308538101
[7] Chatfield C (2003) The analysis of time series: an introduction, 6th edn. Chapman & Hall/CRC, Boca Raton · Zbl 1027.62068
[8] Dahlhaus R, Eichler M (2002) Causality and graphical models for multivariate time series and point processes. In: Hutten H, Kroesl P (eds) IFMBE Proceedings EMBEC 2002, vol 3(2), pp 1430–1431
[9] Dufour JM, Renault E (1998) Short run and long run causality in time series: theory. Econometrica 66:1099–1125 · Zbl 1055.62547 · doi:10.2307/2999631
[10] Eichler M (2002) Granger-causality and path diagrams for multivariate time series. Journal of Econometrics (to appear)
[11] Eichler M (2005) A graphical approach for evaluating effective connectivity in neural systems. Philos Trans R Soc B 360:953–967 · doi:10.1098/rstb.2005.1641
[12] Eichler M, Dahlhaus R, Sandkühler J (2003) Partial correlation analysis for the identification of synaptic connections. Biol Cybern 89:289–302 · Zbl 1105.92311 · doi:10.1007/s00422-003-0400-3
[13] Franaszczuk PJ, Bergey GK (1998) Application of the directed transfer function method to mesial and lateral onset temporal lobe seizures. Brain Topogr 11:13–21 · doi:10.1023/A:1022262318579
[14] Franaszczuk PJ, Blinowska KJ, Kowalczyk M (1985) The application of parametric multichannel spectral estimates in the study of electrical brain activity. Biol Cybern 51:239–247 · Zbl 0546.92002 · doi:10.1007/BF00337149
[15] Goebel R, Roebroeck A, Kim DS, Formisano E (2003) Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. Magn Reson Imaging 21:1251–1261 · doi:10.1016/j.mri.2003.08.026
[16] Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:424–438 · Zbl 1366.91115 · doi:10.2307/1912791
[17] Granger CWJ (1980) Testing for causality, a personal viewpoint. J Econ Dynam Control 2:329–352 · doi:10.1016/0165-1889(80)90069-X
[18] Harrison L, Penny WD, Friston KJ (2003) Multivariate autoregressive modeling of fMRI time series. Neuroimage 4:1477–91 · doi:10.1016/S1053-8119(03)00160-5
[19] Harville DA (1997) Matrix algebra from a statistician’s perspective. Springer Berlin Heidelberg, New York · Zbl 0881.15001
[20] Hayo B (1999) Money-output Granger causality revisited: an empirical analysis of EU countries. Appl Econ 31:1489–1501 · doi:10.1080/000368499323355
[21] Hesse W, Möller E, Arnold M, Schack B (2003) The use of time-variant EEG Granger causality for inspecting directed interdependencies of neural assemblies. J Neurosci Methods 124:27–44 · doi:10.1016/S0165-0270(02)00366-7
[22] Hsiao C (1982) Autoregressive modeling and causal ordering of econometric variables. J Econ Dynam Control 4:243–259 · doi:10.1016/0165-1889(82)90015-X
[23] Kamiński M (2005) Determination of transmission patterns in multichannel data. Philos Trans R Soc B 360:947–952 · doi:10.1098/rstb.2005.1636
[24] Kamiński M, Blinowska KJ, Szelenberger W (1997) Topographic analysis of coherence and propagation of EEG activity during sleep and wakefulness. Electroencephalogr Clin Neurophysiol 102: 216–277 · doi:10.1016/S0013-4694(96)95721-5
[25] Kamiński M, Ding M, Truccolo WA, Bressler SL (2001) Evaluating causal relations in neural systems: Granger causality, directed transfer function and statisdtical assessment of significance. Biol Cybern 85:145–157 · Zbl 1160.92314 · doi:10.1007/s004220000235
[26] Kamiński MJ, Blinowska KJ (1991) A new method of the description of the information flow in the brain structures. Biol Cybern 65:203–210 · Zbl 0734.92003 · doi:10.1007/BF00198091
[27] Korzeniewska A, Kasicki S, Kamiński M, Blinowska KJ (1997) Information flow between hippocampus and related structures during various types of rat’s behaviour. J Neurosci Methods 73:49–60 · doi:10.1016/S0165-0270(96)02212-1
[28] Kuś R, Kamiński M, Blinowska KJ (2004) Determination of EEG activity propagation: pair-wise versus multichannel estimate. IEEE Trans Biomed Eng 51:1501–1510 · doi:10.1109/TBME.2004.827929
[29] Liang H, Ding M, Nakamura R, Bressler SL (2000) Causal influences in primate cerebral cortex during visual pattern discrimination. NeuroReport 11:2875–2880 · doi:10.1097/00001756-200009110-00009
[30] Lütkepohl H (1993) Introduction to multiple time series analysis. Springer Berlin Heidelberg, New York · Zbl 0835.62075
[31] Medvedev A, Willoughby JO (1999) Autoregressive modeling of the EEG in systemic kainic acid-induced epileptogenesis. Int J Neurosci 97:149–167 · doi:10.3109/00207459909000657
[32] Pijn JPM, Van Neerven DN, Noest A, Lopes de Silva FH (1991) Chaos or noise in EEG signals: dependence on state and brain site. Electroencephalogr Clin Neurophysiol 79:371–381 · doi:10.1016/0013-4694(91)90202-F
[33] Pijn JPM, Velis DN, van der Heyden MJ, DeGoede J, van Velen CWM, Lopes de Silva FH (1997) Nonlinear dynamics of epileptic seizure on basis of intracranial EEG recordings. Brain Topogr 9:249–270 · doi:10.1007/BF01464480
[34] Reinsel GC (2003) Elements of multivariate time series analysis 2nd edn. Springer Berlin Heidelberg, New York
[35] Sameshima K, Baccalá LA (1999) Using partial directed coherence to describe neuronal ensemble interactions. J Neurosci Methods 94:93–103 · doi:10.1016/S0165-0270(99)00128-4
[36] Sandkühler J, Eblen-Zajjur AA (1994) Identification and characterization of rhythmic nociceptive and non-reciceptive spinal dorsal horn neurons in the rat. Neuroscience 61:991–1006 · doi:10.1016/0306-4522(94)90419-7
[37] Schack B, Rappelsberger P, Weiss S, Möller E (1999) Adaptive phase estimation and its application in EEG analysis of word processing. J Neurosci Methods 93:49–59 · doi:10.1016/S0165-0270(99)00117-X
[38] Schelter B, Winterhalder M, Eichler M, Peifer M, Hellwig B, Guschlbauer B, Lücking CH, Dahlhaus R, Timmer J (2005) Testing for directed influences in neuroscience using partial directed coherence. J Neurosci Methods (in press)
[39] Sims CA (1980) Macroeconomics and reality. Econometrica 48:1–4 · doi:10.2307/1912017
[40] Stam C, Pijn JPM, Suffczynski P, Lopes da Silva FH (1999) Dynamics of the human alpha rhythm: evidence for non-linearity. Clin Neurophysiol 110:1801–1813 · doi:10.1016/S1388-2457(99)00099-1
[41] Toda HY, Philipps PCB (1993) Vector autoregressions and causality. Econometrica 61:1367–1393 · Zbl 0796.62104 · doi:10.2307/2951647
[42] Valdés-Sosa PA (2004) Spatio-temporal autoregressive models defined over brain manifolds. Neuroinformatics 2:239–250 · doi:10.1385/NI:2:2:239
[43] Veeramani B, Narayanan K, Prasad A, Spanias A, Iasemidis LD (2003) On the use of directed transfer function for nonlinear systems. In: Hamza MH (eds) Simulation and modelling. IASTED/ACTA Press, Calgary, pp 270–274
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.