An Efficient Approach to Graphical Modeling of Time Series

A method for selecting a graphical model for p-vector-valued stationary Gaussian time series was recently proposed by Matsuda and uses the Kullback-Leibler divergence measure to define a test statistic. This statistic was used in a backward selection procedure, but the algorithm is prohibitively expensive for large p. A high degree of sparsity is not assumed. We show that reformulation in terms of a multiple hypothesis test reduces computation time by O(p2) and simulations support the assertion that power levels are attained at least as good as those achieved by Matsuda's much slower approach. Moreover, the new scheme is readily parallelizable for even greater speed gains.

[1]  Jens Timmer,et al.  Cross-spectral Analysis of tremor Time Series , 2000, Int. J. Bifurc. Chaos.

[2]  Lieven Vandenberghe,et al.  Topology Selection in Graphical Models of Autoregressive Processes , 2010, J. Mach. Learn. Res..

[3]  Y. Matsuda.  A test statistic for graphical modelling of multivariate time series , 2006 .

[4]  L. Vandenberghe,et al.  Convex Optimization in Signal Processing and Communications: Graphical models of autoregressive processes , 2009 .

[5]  Helmut Ltkepohl,et al.  New Introduction to Multiple Time Series Analysis , 2007 .

[6]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[7]  Didelez,et al.  Decomposability and selection of graphical models for time series , 2003 .

[8]  Richard A. Davis,et al.  Sparse Vector Autoregressive Modeling , 2012, 1207.0520.

[9]  Yoshihiro Yajima,et al.  Selecting models with different spectral density matrix structures by the cross-validated log likelihood criterion , 2006 .

[10]  Hernando Ombao,et al.  Functional connectivity: Shrinkage estimation and randomization test , 2010, NeuroImage.

[11]  T. Speed,et al.  Gaussian Markov Distributions over Finite Graphs , 1986 .

[12]  Demetrios Kazakos,et al.  Spectral distance measures between Gaussian processes , 1980, ICASSP.

[13]  Lieven Vandenberghe,et al.  Graphical models of autoregressive processes , 2010, Convex Optimization in Signal Processing and Communications.

[14]  Stephen E. Fienberg,et al.  Testing Statistical Hypotheses , 2005 .

[15]  Yan Liu,et al.  An Examination of Practical Granger Causality Inference , 2013, SDM.

[16]  D. Brillinger.  Remarks Concerning Graphical Models for Time Series and Point Processes , 1996 .

[17]  H. Ombao,et al.  The generalized shrinkage estimator for the analysis of functional connectivity of brain signals , 2011, 1108.3187.

[18]  J. Shaffer.  Multiple Hypothesis Testing , 1995 .

[19]  Michael Eichler,et al.  Fitting Graphical Interaction Models to Multivariate Time Series , 2006, UAI.

[20]  R. Dahlhaus.  Graphical interaction models for multivariate time series1 , 2000 .

[21]  Graham J. Wills,et al.  Introduction to graphical modelling , 1995 .

[22]  Wenge Guo.  A note on adaptive Bonferroni and Holm procedures under dependence , 2009 .

[23]  Ursula Gather,et al.  Graphical models for multivariate time series from intensive care monitoring , 2002, Statistics in medicine.

[24]  A. T. Walden,et al.  Graphical modelling for brain connectivity via partial coherence , 2009, Journal of Neuroscience Methods.

[25]  Roland Fried,et al.  Decomposability and selection of graphical models for multivariate time series , 2003 .

[26]  A. Walden,et al.  Brain connectivity in positive and negative syndrome schizophrenia , 2010, Neuroscience.

[27]  Michael I. Jordan,et al.  Learning graphical models for stationary time series , 2004, IEEE Transactions on Signal Processing.

[28]  Nanny Wermuth,et al.  Algorithm AS 105: Fitting a Covariance Selection Model to a Matrix , 1977 .