An efficient approach to graphical modeling of time series

IEEE Transactions on Signal Processing

Volumn 63, Issue 12, 2015, Pages 3266-3276

  Wolstenholme, R J ^a   Walden, Andrew T ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Kullback Leibler divergence; multiple hypothesis test; Undirected graph; vector valued time series

Indexed keywords

GRAPHIC METHODS; TIME SERIES;

COMPUTATION TIME; GAUSSIAN TIME SERIES; GRAPHICAL MODEL; KULLBACK LEIBLER DIVERGENCE; MULTIPLE HYPOTHESIS TESTS; SELECTION PROCEDURES; UNDIRECTED GRAPH; VECTOR VALUED;

STATISTICAL TESTS;

EID: 84930227340     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2015.2422679     Document Type: Article

References (27)

1. F. R. Bach and M. I. Jordan, "Learning graphical models for stationary time series," IEEE Trans. Signal Process., vol. 52, no. 8, pp. 2189-2199, 2004.
2. M. T. Bahadori and Y. Liu, "An examination of practical Granger causality inference," in Proc. SIAM Int. Conf. Data Min., Austin, TX, USA, May 2-4, 2013, pp. 467-475.
3. D. R. Brillinger, "Remarks concerning graphical models for time series and point processes," Revista de Econometria (Brazilian Rev. Econometr.), vol. 16, pp. 1-23, 1996.
4. R. Dahlhaus, "Graphical interaction models for multivariate time series," Metrika, vol. 51, pp. 157-172, 2000.
5. R. A. Davis, P. Zang, and T. Zheng, "Sparse vector autoregressive modeling," ArXiv preprint arXiv:1207.0520 [Online]. Available: http:/ /arxiv.org/abs/1207.0520
6. D. M. Edwards, Introduction to Graphical Modelling, 2nd ed. New York, NY, USA: Springer, 2000.
7. M. Eichler, "Fitting graphical interaction models to multivariate time series," in Proc. 22nd Conf. Uncertainty in Artif. Intell., Arlington, VA, USA, 2006, pp. 147-154, AUAI Press.
8. M. Fiecas and H. Ombao, "The generalized shrinkage estimator for the analysis of functional connectivity of brain signals," Ann. Appl. Statist., vol. 5, pp. 1102-1125, 2011.
9. M. Fiecas, H. Ombao, C. Linkletter, W. Thompson, and J. Sanes, "Functional connectivity: Shrinkage estimation and randomization test," NeuroImage, vol. 49, pp. 3005-3014, 2010.
10. R. Fried and V. Didelez, "Decomposability and selection of graphical models for time series," Biometrika, vol. 90, pp. 251-267, 2003.
11. U. Gather, M. Imhoff, and R. Fried, "Graphical models for multivariate time series from intensive care monitoring," Statist. Med., vol. 21, pp. 2685-2701, 2002.
12. W. Guo, "A note on adaptive Bonferroni and Holm procedures under dependence," Biometrika, vol. 96, pp. 1012-1018, 2009.
13. D. Kazakos and P. Papantoni-Kazakos, "Spectral distance measures between Gaussian processes," IEEE Trans. Autom. Control, vol. 25, no. 5, pp. 950-959, 1980.
14. E. L. Lehmann and J. P. Romano, Testing Statistical Hypotheses, 3rd ed. New York, NY, USA: Springer, 2005.
15. H. Lütkepohl, New Introduction to Multiple Time Series Analysis. Berlin, Germany: Springer, 2006.
16. Y. Matsuda, "A test statistic for graphical modelling of multivariate time series," Biometrika, vol. 93, pp. 399-409, 2006.
17. Y. Matsuda, Y. Yajima, and H. Tong, "Selecting models with different spectral density matrix structures by the cross-validated log likelihood criterion," Bernoulli, vol. 12, pp. 221-249, 2006.
18. T. Medkour, A. T. Walden, and A. P. Burgess, "Graphical modelling for brain connectivity via partial coherence," J. Neurosci.Methods, vol. 180, pp. 374-383, 2009.
19. T. Medkour, A. T. Walden, A. P. Burgess, and V. B. Strelets, "Brain connectivity in positive and negative syndrome schizophrenia," Neurosci., vol. 169, pp. 1779-1788, 2010.
20. M. B. Priestley, Spectral Analysis and Time Series. London, UK: Academic Press, 1981.
21. J. P. Shaffer, "Multiple hypothesis testing," Annu. Rev. Psychol., vol. 46, pp. 561-584, 1995.
22. S. Song and P. J. Bickel, "Large vector autoregressions," ArXiv preprint arXiv:1106.3915 [Online]. Available: http://arxiv.org/abs/ 1106.3915
23. J. Songsiri, J. Dahl, and L. Vandenberghe, "Graphical models of autoregressive processes," in Convex Optimization in Signal Processing and Communications, D. P. Palomar and Y. C. Eldar, Eds. Cambridge, U.K.: Cambridge Univ. Press, 2010.
24. J. Songsiri, J. Dahl, and L. Vandenberghe, "Topology selection in graphical models of autoregressive processes," J. Mach. Learn. Res., vol. 11, pp. 2671-2705, 2010.
25. T. P. Speed and H. Kiiveri, "Gaussian Markov distributions over finite graphs," Ann. Statist., vol. 14, pp. 138-150, 1986.
26. J. Timmer et al., "Cross-spectral analysis of tremor time series," Int. J. Bifurcation Chaos, vol. 10, pp. 2595-2610, 2000.
27. N. Wermuth and E. Scheidt, "Fitting a covariance selection model to a matrix," Appl. Statist., vol. 26, pp. 88-92, 1977.