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Popescuit is suggested that a principled bottom-up investigation be undertaken, beginning withthe simple SVAR form studied in this paper and all proposed criteria be quantified:type I, II and III errors, accurate determination of causality strength and direction androbustness in the presence of conditioning variables and colored mixed noise.AcknowledgmentsI would like to thank Guido Nolte for his insightful feedback and informative discussions.ReferencesH. Akaike. On the use of a linear model for the identification of feedback systems.Annals of the Institute of statistical mathematics, 20(1):425–439, 1968.L. A Baccalá and K. Sameshima. Partial directed coherence: a new concept in neuralstructure determination. Biological cybernetics, 84(6):463–474, 2001.L. A. Baccalá, M. A. Nicolelis, C. H. Yu, and M. Oshiro. Structural analysis of neuralcircuits using the theory of directed graphs. Computers and Biomedical Research,an International Journal, 24:7–28, Feb 1991. URL http://www.ncbi.nlm.nih.gov/pubmed/2004525.A. B. Barrett, L. Barnett, and A. K. Seth. Multivariate granger causality and generalizedvariance. Physical Review E, 81(4):041907, April 2010. doi: 10.1103/PhysRevE.81.041907. URL http://link.aps.org/doi/10.1103/PhysRevE.81.041907.B. S. Bernanke, J. Boivin, and P. Eliasz. Measuring the Effects of Monetary Policy: AFactor-Augmented Vector Autoregressive (FAVAR) Approach. Quarterly Journal ofEconomics, 120(1):387–422, 2005.K. J. Blinowska, R. Kuś, and M. Kamiński. Granger causality and informationflow in multivariate processes. Physical Review E, 70(5):050902, November 2004.doi: 10.1103/PhysRevE.70.050902. URL http://link.aps.org/doi/10.1103/PhysRevE.70.050902.P. E. Caines. Weak and strong feedback free processes. IEEE. Trans. Autom . Contr,21:737–739, 1976.N. Chlaß and A. Moneta. Can Graphical Causal Inference Be Extended to NonlinearSettings? EPSA Epistemology and Methodology of Science, pages 63–72, 2010.T. Chu and C. Glymour. Search for additive nonlinear time series causal models. TheJournal of Machine Learning Research, 9:967–991, 2008.66
Robust Statistics for CausalityR. A. Fisher. Statistical Methods for Research Workers. Macmillan Pub Co, 1925.ISBN 0028447301.W. Gersch and G. V. Goddard. Epileptic focus location: spectral analysis method.Science (New York, N.Y.), 169(946):701–702, August 1970. ISSN 0036-8075. URLhttp://www.ncbi.nlm.nih.gov/pubmed/5429908. PMID: 5429908.J. Geweke. Measurement of linear dependence and feedback between multiple timeseries. Journal of the American Statistical Association, 77:304–313, 1982.G. Gigerenzer, Z. Swijtink, T. Porter, L. Daston, J. Beatty, and L. Kruger. The Empireof Chance: How Probability Changed Science and Everyday Life. CambridgeUniversity Press, October 1990. ISBN 052139838X.C. W. J. Granger. Investigating causal relations by econometric models and crossspectralmethods. Econometrica, 37(3):424–438, August 1969. ISSN 00129682.URL http://www.jstor.org/stable/1912791.I. Guyon. Time series analysis with the causality workbench. Journal of MachineLearning Research, Workshop and Conference Proceedings, XX. Time SeriesCausality:XX–XX, 2011.I. Guyon and A. Elisseeff. An introduction to variable and feature selection. JMLR, 3:1157–1182, March 2003.I. Guyon, C. Aliferis, G. Cooper, A. Elisseeff, J.-P. Pellet, P. Spirtes, and A. Statnikov.Design and analysis of the causation and prediction challenge. wcci2008 workshopon causality, hong kong, june 3-4 2008. Journal of Machine Learning ResearchWorkshop and Conference Proceedings, 3:1–33, 2008.I. Guyon, D. Janzing, and B. Schölkopf. Causality: Objectives and assessment. JMLRW&CP, 6:1–38, 2010.P. O. Hoyer, D. Janzing, J. M. Mooij, J. Peters, and B. Schölkopf. Nonlinear causaldiscovery with additive noise models. In D. Koller, D. Schuurmans, Y. Bengio, andL. Bottou, editors, Advances in Neural Information Processing Systems 21, pages689–696, 2009.M Kaminski, M Ding, W A Truccolo, and S L Bressler. Evaluating causal relationsin neural systems: granger causality, directed transfer function and statistical assessmentof significance. Biological Cybernetics, 85(2):145–157, August 2001. ISSN0340-1200. URL http://www.ncbi.nlm.nih.gov/pubmed/11508777.PMID: 11508777.M. J. Kaminski and K. J. Blinowska. A new method of the description of the informationflow in the brain structures. Biological Cybernetics, 65(3):203–210, 1991. ISSN0340-1200. doi: 10.1007/BF00198091. URL http://dblp.uni-trier.de/rec/bibtex/journals/bc/KaminskiB91.67
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Causality in Time SeriesVolume 5:Ca
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PrefaceThe following is a print ver
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JMLR: Workshop and Conference Proce
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Linking Granger Causality and the P
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Page 44 and 45: Popescugeneral terms, if we are pre
Page 46 and 47: PopescuType III error prob. γ = P
Page 48 and 49: Popescuwhich would correspond to a
Page 50 and 51: Popescuvalued vector. A Data Genera
Page 52 and 53: Popescuy i =K∑︁A k y i−k + Bu
Page 54 and 55: Popescuy i =K∑︁A k y i−k + Bu
Page 56 and 57: PopescuFigure 1: SVAR causality and
Page 58 and 59: Popescu6. Spectral methods and phas
Page 60 and 61: PopescuH GCj→i|u = logD i − log
Page 62 and 63: Popescu8.1. The cardinal transform
Page 64 and 65: Popescuy N,i = Bx N,i (37)y = (1
Page 66 and 67: Popescu(a) Unmixed colored noise(b)
Page 68 and 69: PopescuAs we can see in both Figure
Page 70 and 71: Popescuβ > 0 y C,i =x N,i =⎡K∑
Page 72 and 73: Popescupretation of information flo
Page 76 and 77: PopescuA. N. Kolmogorov and A. N. S
Page 78 and 79: PopescuH. White and X. Lu. Granger
Page 80 and 81: PopescuTable 6: α vs. ΨN * → 50
Page 82 and 83: Roebroeck Seth Valdes-Sosaincreasin
Page 84 and 85: Roebroeck Seth Valdes-SosaFigure 1:
Page 86 and 87: Roebroeck Seth Valdes-Sosasignal fr
Page 88 and 89: Roebroeck Seth Valdes-Sosablood flo
Page 90 and 91: Roebroeck Seth Valdes-Sosaat lower
Page 92 and 93: Roebroeck Seth Valdes-SosaTable 1:
Page 94 and 95: Roebroeck Seth Valdes-Sosa1984) and
Page 96 and 97: Roebroeck Seth Valdes-Sosaanalysis
Page 98 and 99: Roebroeck Seth Valdes-Sosamarginal
Page 100 and 101: Roebroeck Seth Valdes-SosaThe initi
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Page 114 and 115: Moneta Chlass Entner HoyerA traditi
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Page 120 and 121: Moneta Chlass Entner HoyerThe Wald
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Moneta Chlass Entner Hoyerthe struc
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Moneta Chlass Entner Hoyerstricted
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Moneta Chlass Entner Hoyerwhere h 1
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Moneta Chlass Entner Hoyerlatter re
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Moneta Chlass Entner Hoyercausal mo
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Moneta Chlass Entner HoyerL. Baring
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Moneta Chlass Entner HoyerS. Johans
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Moneta Chlass Entner HoyerA. Yatche
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Guyon Statnikov Aliferisis extremel
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Guyon Statnikov Aliferis4. A Data R
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Guyon Statnikov Aliferismethods on
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Guyon Statnikov Aliferisvolume 3, p
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