TY - JOUR

T1 - Granger causality in the frequency domain

T2 - Derivation and applications

AU - Lima, Vinicius

AU - Dellajustina, Fernanda Jaiara

AU - Shimoura, Renan O.

AU - Girardi-Schappo, Mauricio

AU - Kamiji, Nilton L.

AU - Pena, Rodrigo F.O.

AU - Roque, Antonio C.

N1 - Funding Information:
This article was produced as part of the S. Paulo Research Foundation (FAPESP) Research, Innovation and Dissemination Center for Neuromathematics (CEPID NeuroMat, Grant No. 2013/07699-0). The authors also thank FAPESP support through Grants No. 2013/25667-8 (R.F.O.P.), 2015/50122-0 (A.C.R.), 2016/03855-5 (N.L.K.), 2017/07688-9 (R.O.S), 2018/20277-0 (A.C.R.) and 2018/09150-9 (M.G.-S.). V.L. is supported by a CAPES PhD scholarship. A.C.R. thanks financial support from the National Council of Scientific and Technological Development (CNPq), Grant No. 306251/2014-0. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
Publisher Copyright:
© Sociedade Brasileira de Física.

PY - 2020

Y1 - 2020

N2 - Physicists are starting to work in areas where noisy signal analysis is required. In these fields, such as Economics, Neuroscience, and Physics, the notion of causality should be interpreted as a statistical measure. We introduce to the lay reader the Granger causality between two time series and illustrate ways of calculating it: a signal X "Granger-causes" a signal Y if the observation of the past of X increases the predictability of the future of Y when compared to the same prediction done with the past of Y alone. In other words, for Granger causality between two quantities it suffices that information extracted from the past of one of them improves the forecast of the future of the other, even in the absence of any physical mechanism of interaction. We present derivations of the Granger causality measure in the time and frequency domains and give numerical examples using a non-parametric estimation method in the frequency domain. Parametric methods are addressed in the Appendix. We discuss the limitations and applications of this method and other alternatives to measure causality.

AB - Physicists are starting to work in areas where noisy signal analysis is required. In these fields, such as Economics, Neuroscience, and Physics, the notion of causality should be interpreted as a statistical measure. We introduce to the lay reader the Granger causality between two time series and illustrate ways of calculating it: a signal X "Granger-causes" a signal Y if the observation of the past of X increases the predictability of the future of Y when compared to the same prediction done with the past of Y alone. In other words, for Granger causality between two quantities it suffices that information extracted from the past of one of them improves the forecast of the future of the other, even in the absence of any physical mechanism of interaction. We present derivations of the Granger causality measure in the time and frequency domains and give numerical examples using a non-parametric estimation method in the frequency domain. Parametric methods are addressed in the Appendix. We discuss the limitations and applications of this method and other alternatives to measure causality.

KW - Autoregressive process

KW - Conditional granger causality

KW - Granger causality

KW - Non-parametric estimation

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U2 - 10.1590/1806-9126-RBEF-2020-0007

DO - 10.1590/1806-9126-RBEF-2020-0007

M3 - Article

AN - SCOPUS:85091532633

SN - 0102-4744

VL - 42

JO - Revista Brasileira de Ensino de Fisica

JF - Revista Brasileira de Ensino de Fisica

M1 - e20200007

ER -