Multivariate autoregressive models

Functional neuroimaging has been used to corroborate functional specialization as a principle of organization in the human brain. However, disparate regions of the brain do not operate in isolation and, more recently, neuroimaging has been used to characterize the network properties of the brain under speci.c cognitive states Buchel and Friston, 1997a  and  Buchel and Friston, 2000 . These studies address a complementary principle of organization, functional integration.

[1]  G. Box,et al.  Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , 1970 .

[2]  Katarzyna J. Blinowska,et al.  A new method of the description of the information flow in the brain structures , 1991, Biological Cybernetics.

[3]  Karl J. Friston,et al.  Psychophysiological and Modulatory Interactions in Neuroimaging , 1997, NeuroImage.

[4]  R. Muirhead Aspects of Multivariate Statistical Theory , 1982, Wiley Series in Probability and Statistics.

[5]  B. Porat,et al.  Digital Spectral Analysis with Applications. , 1988 .

[6]  Laura Astolfi,et al.  Assessing cortical functional connectivity by partial directed coherence: simulations and application to real data , 2006, IEEE Transactions on Biomedical Engineering.

[7]  J. Maunsell,et al.  Neuronal correlates of inferred motion in primate posterior parietal cortex , 1995, Nature.

[8]  Arnold Neumaier,et al.  Estimation of parameters and eigenmodes of multivariate autoregressive models , 2001, TOMS.

[9]  Michael Eichler,et al.  A graphical approach for evaluating effective connectivity in neural systems , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[10]  Karl J. Friston,et al.  Time‐dependent changes in effective connectivity measured with PET , 1993 .

[11]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[12]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics , 1991 .

[13]  Karl J. Friston Brain function, nonlinear coupling, and neuronal transients. , 2001, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[14]  S. Weisberg Applied Linear Regression , 1981 .

[15]  G. C. Tiao,et al.  Modeling Multiple Time Series with Applications , 1981 .

[16]  M. B. Priestley,et al.  Non-linear and non-stationary time series analysis , 1990 .

[17]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[18]  Karl J. Friston,et al.  Attentional modulation of effective connectivity from V2 to V5/MT in humans. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Karl J. Friston,et al.  Assessing interactions among neuronal systems using functional neuroimaging , 2000, Neural Networks.

[20]  J. Pearl Graphs, Causality, and Structural Equation Models , 1998 .

[21]  Laura Astolfi,et al.  Tracking the Time-Varying Cortical Connectivity Patterns by Adaptive Multivariate Estimators , 2008, IEEE Transactions on Biomedical Engineering.

[22]  M. Kaminski,et al.  Topographic analysis of coherence and propagation of EEG activity during sleep and wakefulness. , 1997, Electroencephalography and clinical neurophysiology.

[23]  C. Büchel,et al.  Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI. , 1997, Cerebral cortex.

[24]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.

[25]  Karl J. Friston Book Review: Brain Function, Nonlinear Coupling, and Neuronal Transients , 2001 .

[26]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[27]  C. Granger Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[28]  A. Treisman,et al.  Voluntary Attention Modulates fMRI Activity in Human MT–MST , 1997, Neuron.

[29]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition) , 1999 .

[30]  Minh Q. Phan,et al.  Identification and control of mechanical systems , 2001 .

[31]  Karl J. Friston The labile brain. I. Neuronal transients and nonlinear coupling. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[32]  William D. Penny,et al.  Bayesian nonstationary autoregressive models for biomedical signal analysis , 2002, IEEE Transactions on Biomedical Engineering.

[33]  Leslie G. Ungerleider,et al.  Network analysis of cortical visual pathways mapped with PET , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[34]  Chris Chatfield,et al.  The Analysis of Time Series , 1990 .

[35]  Karl J. Friston,et al.  Characterizing modulatory interactions between areas V1 and V2 in human cortex: A new treatment of functional MRI data , 1994 .

[36]  S. Roberts,et al.  Bayesian multivariate autoregressive models with structured priors , 2002 .

[37]  Mingzhou Ding,et al.  Investigation of cooperative cortical dynamics by multivariate autoregressive modeling of event-related local field potentials , 1999, Neurocomputing.

[38]  C. Büchel,et al.  Dynamic changes in effective connectivity characterized by variable parameter regression and kalman filtering , 1998, Human brain mapping.

[39]  A. I. McLeod,et al.  Distribution of the Residual Autocorrelations in Multivariate Arma Time Series Models , 1981 .

[40]  H. Lütkepohl COMPARISON OF CRITERIA FOR ESTIMATING THE ORDER OF A VECTOR AUTOREGRESSIVE PROCESS , 1985 .

[41]  H. Storch,et al.  Statistical Analysis in Climate Research , 2000 .

[42]  Gabriele Lohmann,et al.  On Multivariate Spectral Analysis of fMRI Time Series , 2001, NeuroImage.

[43]  James D. Hamilton Time Series Analysis , 1994 .

[44]  Karl J. Friston,et al.  Human Brain Function , 1997 .

[45]  Lester Melie-García,et al.  Estimating brain functional connectivity with sparse multivariate autoregression , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.