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Volumn 81, Issue 4, 2010, Pages

Multivariate Granger causality and generalized variance

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX SYSTEMS; EXPERIMENTAL DATA; FUNCTIONAL RELATION; GENERALIZED VARIANCE; GRANGER CAUSALITY; RESIDUAL ERROR; SINGLE VARIABLE; UNIVARIATE;

EID: 77951117702     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.041907     Document Type: Article
Times cited : (215)

References (56)
  • 1
    • 37649012219 scopus 로고    scopus 로고
    • in edited by S. Schelter, M. Winterhalder, and J. Timmer (Wiley, Wienheim
    • M. Ding, Y. Chen, and S. Bressler, in Handbook of Time Series Analysis, edited by, S. Schelter, M. Winterhalder, and, J. Timmer, (Wiley, Wienheim, 2006), pp. 438-460.
    • (2006) Handbook of Time Series Analysis , pp. 438-460
    • Ding, M.1    Chen, Y.2    Bressler, S.3
  • 3
    • 12944275674 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.85.461
    • T. Schreiber, Phys. Rev. Lett. 85, 461 (2000). 10.1103/PhysRevLett.85.461
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 461
    • Schreiber, T.1
  • 7
    • 1642306434 scopus 로고
    • in edited by E. F. Beckenbach (McGraw Hill, New York
    • N. Wiener, in Modern Mathematics for Engineers, edited by, E. F. Beckenbach, (McGraw Hill, New York, 1956).
    • (1956) Modern Mathematics for Engineers
    • Wiener, N.1
  • 8
    • 0000351727 scopus 로고
    • 10.2307/1912791
    • C. W. J. Granger, Econometrica 37, 424 (1969). 10.2307/1912791
    • (1969) Econometrica , vol.37 , pp. 424
    • Granger, C.W.J.1
  • 10
    • 74149089224 scopus 로고    scopus 로고
    • 10.1016/j.jneumeth.2009.11.020
    • A. K. Seth, J. Neurosci. Methods 186, 262 (2010). 10.1016/j.jneumeth. 2009.11.020
    • (2010) J. Neurosci. Methods , vol.186 , pp. 262
    • Seth, A.K.1
  • 11
    • 69949109309 scopus 로고    scopus 로고
    • 10.1007/s12559-009-9007-x
    • A. K. Seth, Cognitive Computation 1 (1), 50-63 (2009). 10.1007/s12559-009-9007-x
    • (2009) Cognitive Computation , vol.1 , Issue.1 , pp. 50-63
    • Seth, A.K.1
  • 12
    • 33745595378 scopus 로고    scopus 로고
    • 10.1080/09548980500238756
    • A. K. Seth, Network 16, 35 (2005). 10.1080/09548980500238756
    • (2005) Network , vol.16 , pp. 35
    • Seth, A.K.1
  • 13
    • 77949475448 scopus 로고    scopus 로고
    • 10.1162/artl.2010.16.2.16204
    • A. K. Seth, Artif. Life 16, 179 (2009). 10.1162/artl.2010.16.2.16204
    • (2009) Artif. Life , vol.16 , pp. 179
    • Seth, A.K.1
  • 15
    • 77951098953 scopus 로고    scopus 로고
    • This is to be distinguished from the conditional covariance, which will in general be a random variable, though later we note that for Gaussian variables the notions coincide.
    • This is to be distinguished from the conditional covariance, which will in general be a random variable, though later we note that for Gaussian variables the notions coincide.
  • 17
    • 77951102201 scopus 로고    scopus 로고
    • While our analysis may be extended to continuous time we focus here on the discrete-time case.
    • While our analysis may be extended to continuous time we focus here on the discrete-time case.
  • 18
    • 77951126725 scopus 로고    scopus 로고
    • Here and in the remainder of this paper we assume, without loss of generality, that all random vectors and random processes have zero mean; thus constant terms are omitted in all linear regressions.
    • Here and in the remainder of this paper we assume, without loss of generality, that all random vectors and random processes have zero mean; thus constant terms are omitted in all linear regressions.
  • 19
    • 77951137036 scopus 로고    scopus 로고
    • The analysis carries through for the nonstationary case, but for simplicity we assume here that all processes are stationary.
    • The analysis carries through for the nonstationary case, but for simplicity we assume here that all processes are stationary.
  • 20
    • 77951142596 scopus 로고    scopus 로고
    • This might be more familiar as conditional G-causality, with Z as the conditioning variable. In practice it is the more useful form; for the nonconditional version, Z may simply be omitted.
    • This might be more familiar as conditional G-causality, with Z as the conditioning variable. In practice it is the more useful form; for the nonconditional version, Z may simply be omitted.
  • 21
    • 77951112230 scopus 로고    scopus 로고
    • - will generally be multivariate (at least if p,q>1); hence they are written in bold type.
    • - will generally be multivariate (at least if p, q > 1); hence they are written in bold type.
  • 22
    • 77951124543 scopus 로고    scopus 로고
    • We remark that for significance testing of G-causality it is quite common to use the appropriate F statistic for regressions rather than FY→X Z itself; the quantities are in any case related by a monotonic transformation.
    • We remark that for significance testing of G-causality it is quite common to use the appropriate F statistic for regressions rather than F Y → X Z itself; the quantities are in any case related by a monotonic transformation.
  • 23
    • 0001805137 scopus 로고
    • 10.1016/S0019-9958(63)90092-5
    • C. W. J. Granger, Inf. Control. 6, 28 (1963). 10.1016/S0019-9958(63) 90092-5
    • (1963) Inf. Control. , vol.6 , pp. 28
    • Granger, C.W.J.1
  • 27
    • 0036610922 scopus 로고    scopus 로고
    • 10.1016/S0167-2789(02)00432-3
    • A. Kaiser and T. Schreiber, Physica D 166, 43 (2002). 10.1016/S0167-2789(02)00432-3
    • (2002) Physica D , vol.166 , pp. 43
    • Kaiser, A.1    Schreiber, T.2
  • 30
    • 77951134869 scopus 로고    scopus 로고
    • If the predictee variable has a continuous (multivariate) distribution, we note that the Jacobian determinants in the standard change-of-variables formula for entropy calculation cancel out.
    • If the predictee variable has a continuous (multivariate) distribution, we note that the Jacobian determinants in the standard change-of-variables formula for entropy calculation cancel out.
  • 35
    • 77951113343 scopus 로고    scopus 로고
    • - ) which appears in FY→X (using a finite number of lags will generally result in an overestimate of FY→X since residual errors will be larger than for the exact regression). As applied to empirical data, it is in any case good practice to choose "sufficient" lags for all regressions so as to model the data adequately without overfitting.
    • -) which appears in F Y → X (using a finite number of lags will generally result in an overestimate of F Y → X since residual errors will be larger than for the exact regression). As applied to empirical data, it is in any case good practice to choose "sufficient" lags for all regressions so as to model the data adequately without overfitting.
  • 38
    • 77951116527 scopus 로고    scopus 로고
    • In it is stated that partial G-causality may in some circumstances be negative; the justification for this is unclear.
    • In it is stated that partial G-causality may in some circumstances be negative; the justification for this is unclear.
  • 39
    • 77951107258 scopus 로고    scopus 로고
    • In, under the section headed "partial complex Granger causality," the quantity developed appears to be (the trace version of) what is conventionally referred to as conditional G-causality rather than partial G-causality as introduced in and referenced in this section.
    • In, under the section headed "partial complex Granger causality," the quantity developed appears to be (the trace version of) what is conventionally referred to as conditional G-causality rather than partial G-causality as introduced in and referenced in this section.
  • 40
    • 77951094499 scopus 로고    scopus 로고
    • This is the "weighted" version of causal density. An unweighted and [0,1] bounded alternative can be defined as the fraction of all pairwise conditional causalities that are statistically significant at a given significance level.
    • This is the "weighted" version of causal density. An unweighted and [0,1] bounded alternative can be defined as the fraction of all pairwise conditional causalities that are statistically significant at a given significance level.
  • 41
    • 67049132019 scopus 로고    scopus 로고
    • 10.4249/scholarpedia.1623
    • O. Sporns, Scholarpedia J. 2, 1623 (2007). 10.4249/scholarpedia.1623
    • (2007) Scholarpedia J. , vol.2 , pp. 1623
    • Sporns, O.1
  • 43
    • 56149119251 scopus 로고    scopus 로고
    • 10.1103/PhysRevE.78.041924
    • M. Shanahan, Phys. Rev. E 78, 041924 (2008). 10.1103/PhysRevE.78.041924
    • (2008) Phys. Rev. e , vol.78 , pp. 041924
    • Shanahan, M.1
  • 45
    • 61949486330 scopus 로고    scopus 로고
    • in edited by James Tomberlin (Oxford: Blackwell Publishers, Oxford, UK
    • M. A. Bedau, in Philosophical Perspectives: Mind, Causation, and World, edited by, James Tomberlin, (Oxford: Blackwell Publishers, Oxford, UK, 1997), 11, 375.
    • (1997) Philosophical Perspectives: Mind, Causation, and World , vol.11 , pp. 375
    • Bedau, M.A.1
  • 46
    • 77951095021 scopus 로고    scopus 로고
    • e-print arXiv:cond-mat/0303625.
    • C. Shalizi and C. Moore, e-print arXiv:cond-mat/0303625.
    • Shalizi, C.1    Moore, C.2
  • 48
    • 55149125233 scopus 로고    scopus 로고
    • 10.4249/scholarpedia.1667
    • A. K. Seth, Scholarpedia J. 2, 1667 (2007). 10.4249/scholarpedia.1667
    • (2007) Scholarpedia J. , vol.2 , pp. 1667
    • Seth, A.K.1
  • 51
    • 77951113632 scopus 로고    scopus 로고
    • In approximation.
    • In approximation.
  • 56
    • 0000120766 scopus 로고
    • 10.1214/aos/1176344136
    • G. Schwarz, Ann. Stat. 6, 461 (1978). 10.1214/aos/1176344136
    • (1978) Ann. Stat. , vol.6 , pp. 461
    • Schwarz, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.